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Pedro L. D. Peres - One of the best experts on this subject based on the ideXlab platform.
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ℋ 2 filter design through multi simplex modeling for discrete time markov jump linear systems with partly unknown Transition Probability Matrix
Conference on Decision and Control, 2014Co-Authors: Cecília F. Morais, Márcio F. Braga, Ricardo C. L. F. Oliveira, Marcio J Lacerda, Pedro L. D. PeresAbstract:This paper is concerned with the ℋ 2 robust filtering problem for discrete-time Markov jump linear systems (MJLS) with Transition Probability Matrix affected by uncertainties. Differently from previous approaches in the literature, the proposed strategy presents a systematic way to handle, simultaneously, different types of uncertainties commonly appearing in the Transition Probability Matrix of MJLS. Fullorder filters with partial, complete or null Markov mode observation are synthesized via a linear Matrix inequality (LMI) based formulation. The main novelty of the proposed filter design procedure is the use of parameter-dependent Lyapunov matrices of arbitrary degree to certify the stochastic stability and to guarantee an upper bound to the ℋ 2 norm of the filtering error system. Moreover, the proposed conditions also include slack variables and scalars. For fixed values of the scalar parameters, the conditions become LMIs. Numerical examples borrowed from the literature illustrate that the proposed filter can provide better ℋ 2 guaranteed costs when compared to other existing methods.
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ℋ∞ static output feedback control of discrete-time Markov jump linear systems with uncertain Transition Probability Matrix
2014 American Control Conference, 2014Co-Authors: Cecília F. Morais, Márcio F. Braga, Ricardo C. L. F. Oliveira, Pedro L. D. PeresAbstract:This paper investigates the problem of ℋ∞ static output feedback control design for discrete-time Markov jump linear systems (MJLS), assuming that the Transition Probability Matrix is not precisely known, but affected by different classes of uncertainties: polytopic, bounded or completely unknown elements. All types of uncertainties are modeled through one single representation, expressed in terms of the Cartesian product of simplexes, called multi-simplex. The main novelty of the proposed design procedure is that, differently from previous approaches in the literature, parameter-dependent Lyapunov matrices are used to certify the closed-loop stability with an ℋ∞ bound for the discrete-time MJLS. The proposed conditions are based on linear Matrix inequality relaxations performed in two steps: the first step generates a parameter-dependent state feedback controller that is employed as an input for the second stage, which synthesizes a robust static output feedback gain assuring an ℋ∞ guaranteed cost. The proposed strategy can also cope with ℋ∞ state feedback control for discrete-time MJLS. Numerical examples illustrate the advantages of the proposed methodology when compared to other methods from the literature.
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CDC - ℋ 2 filter design through multi-simplex modeling for discrete-time Markov jump linear systems with partly unknown Transition Probability Matrix
53rd IEEE Conference on Decision and Control, 2014Co-Authors: Cecília F. Morais, Márcio F. Braga, Ricardo C. L. F. Oliveira, Marcio J Lacerda, Pedro L. D. PeresAbstract:This paper is concerned with the ℋ 2 robust filtering problem for discrete-time Markov jump linear systems (MJLS) with Transition Probability Matrix affected by uncertainties. Differently from previous approaches in the literature, the proposed strategy presents a systematic way to handle, simultaneously, different types of uncertainties commonly appearing in the Transition Probability Matrix of MJLS. Fullorder filters with partial, complete or null Markov mode observation are synthesized via a linear Matrix inequality (LMI) based formulation. The main novelty of the proposed filter design procedure is the use of parameter-dependent Lyapunov matrices of arbitrary degree to certify the stochastic stability and to guarantee an upper bound to the ℋ 2 norm of the filtering error system. Moreover, the proposed conditions also include slack variables and scalars. For fixed values of the scalar parameters, the conditions become LMIs. Numerical examples borrowed from the literature illustrate that the proposed filter can provide better ℋ 2 guaranteed costs when compared to other existing methods.
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***ℋ∞ Filter Design through Multi-simplex Modeling for Discrete-time Markov Jump Linear Systems with Partly Unknown Transition Probability Matrix
IFAC Proceedings Volumes, 2014Co-Authors: Cecília F. Morais, Márcio F. Braga, Ricardo C. L. F. Oliveira, Marcio J Lacerda, Pedro L. D. PeresAbstract:Abstract This paper addresses the problem of *** ℋ ∞ filter design for discrete-time Markov jump linear systems (MJLS) with Transition Probability Matrix affected by uncertainties. The proposed methodology allows to take into account the different types of uncertainties usually adopted in MJLS in a systematic way. New conditions are given for *** ℋ ∞ filter design with partial, complete or null Markov mode availability. Due to the presence of slack variables in the synthesis conditions and to the use of homogeneous polynomial solutions of arbitrary degrees, less conservative linear Matrix inequality relaxations can be obtained. Numerical experiments illustrate the better performance and efficiency of the proposed approach when compared to other strategies available in the literature.
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ACC - ℋ ∞ static output feedback control of discrete-time Markov jump linear systems with uncertain Transition Probability Matrix
2014 American Control Conference, 2014Co-Authors: Cecília F. Morais, Márcio F. Braga, Ricardo C. L. F. Oliveira, Pedro L. D. PeresAbstract:This paper investigates the problem of ℋ ∞ static output feedback control design for discrete-time Markov jump linear systems (MJLS), assuming that the Transition Probability Matrix is not precisely known, but affected by different classes of uncertainties: polytopic, bounded or completely unknown elements. All types of uncertainties are modeled through one single representation, expressed in terms of the Cartesian product of simplexes, called multi-simplex. The main novelty of the proposed design procedure is that, differently from previous approaches in the literature, parameter-dependent Lyapunov matrices are used to certify the closed-loop stability with an ℋ ∞ bound for the discrete-time MJLS. The proposed conditions are based on linear Matrix inequality relaxations performed in two steps: the first step generates a parameter-dependent state feedback controller that is employed as an input for the second stage, which synthesizes a robust static output feedback gain assuring an ℋ ∞ guaranteed cost. The proposed strategy can also cope with ℋ ∞ state feedback control for discrete-time MJLS. Numerical examples illustrate the advantages of the proposed methodology when compared to other methods from the literature.
Cecília F. Morais - One of the best experts on this subject based on the ideXlab platform.
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ℋ 2 filter design through multi simplex modeling for discrete time markov jump linear systems with partly unknown Transition Probability Matrix
Conference on Decision and Control, 2014Co-Authors: Cecília F. Morais, Márcio F. Braga, Ricardo C. L. F. Oliveira, Marcio J Lacerda, Pedro L. D. PeresAbstract:This paper is concerned with the ℋ 2 robust filtering problem for discrete-time Markov jump linear systems (MJLS) with Transition Probability Matrix affected by uncertainties. Differently from previous approaches in the literature, the proposed strategy presents a systematic way to handle, simultaneously, different types of uncertainties commonly appearing in the Transition Probability Matrix of MJLS. Fullorder filters with partial, complete or null Markov mode observation are synthesized via a linear Matrix inequality (LMI) based formulation. The main novelty of the proposed filter design procedure is the use of parameter-dependent Lyapunov matrices of arbitrary degree to certify the stochastic stability and to guarantee an upper bound to the ℋ 2 norm of the filtering error system. Moreover, the proposed conditions also include slack variables and scalars. For fixed values of the scalar parameters, the conditions become LMIs. Numerical examples borrowed from the literature illustrate that the proposed filter can provide better ℋ 2 guaranteed costs when compared to other existing methods.
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ℋ∞ static output feedback control of discrete-time Markov jump linear systems with uncertain Transition Probability Matrix
2014 American Control Conference, 2014Co-Authors: Cecília F. Morais, Márcio F. Braga, Ricardo C. L. F. Oliveira, Pedro L. D. PeresAbstract:This paper investigates the problem of ℋ∞ static output feedback control design for discrete-time Markov jump linear systems (MJLS), assuming that the Transition Probability Matrix is not precisely known, but affected by different classes of uncertainties: polytopic, bounded or completely unknown elements. All types of uncertainties are modeled through one single representation, expressed in terms of the Cartesian product of simplexes, called multi-simplex. The main novelty of the proposed design procedure is that, differently from previous approaches in the literature, parameter-dependent Lyapunov matrices are used to certify the closed-loop stability with an ℋ∞ bound for the discrete-time MJLS. The proposed conditions are based on linear Matrix inequality relaxations performed in two steps: the first step generates a parameter-dependent state feedback controller that is employed as an input for the second stage, which synthesizes a robust static output feedback gain assuring an ℋ∞ guaranteed cost. The proposed strategy can also cope with ℋ∞ state feedback control for discrete-time MJLS. Numerical examples illustrate the advantages of the proposed methodology when compared to other methods from the literature.
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CDC - ℋ 2 filter design through multi-simplex modeling for discrete-time Markov jump linear systems with partly unknown Transition Probability Matrix
53rd IEEE Conference on Decision and Control, 2014Co-Authors: Cecília F. Morais, Márcio F. Braga, Ricardo C. L. F. Oliveira, Marcio J Lacerda, Pedro L. D. PeresAbstract:This paper is concerned with the ℋ 2 robust filtering problem for discrete-time Markov jump linear systems (MJLS) with Transition Probability Matrix affected by uncertainties. Differently from previous approaches in the literature, the proposed strategy presents a systematic way to handle, simultaneously, different types of uncertainties commonly appearing in the Transition Probability Matrix of MJLS. Fullorder filters with partial, complete or null Markov mode observation are synthesized via a linear Matrix inequality (LMI) based formulation. The main novelty of the proposed filter design procedure is the use of parameter-dependent Lyapunov matrices of arbitrary degree to certify the stochastic stability and to guarantee an upper bound to the ℋ 2 norm of the filtering error system. Moreover, the proposed conditions also include slack variables and scalars. For fixed values of the scalar parameters, the conditions become LMIs. Numerical examples borrowed from the literature illustrate that the proposed filter can provide better ℋ 2 guaranteed costs when compared to other existing methods.
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***ℋ∞ Filter Design through Multi-simplex Modeling for Discrete-time Markov Jump Linear Systems with Partly Unknown Transition Probability Matrix
IFAC Proceedings Volumes, 2014Co-Authors: Cecília F. Morais, Márcio F. Braga, Ricardo C. L. F. Oliveira, Marcio J Lacerda, Pedro L. D. PeresAbstract:Abstract This paper addresses the problem of *** ℋ ∞ filter design for discrete-time Markov jump linear systems (MJLS) with Transition Probability Matrix affected by uncertainties. The proposed methodology allows to take into account the different types of uncertainties usually adopted in MJLS in a systematic way. New conditions are given for *** ℋ ∞ filter design with partial, complete or null Markov mode availability. Due to the presence of slack variables in the synthesis conditions and to the use of homogeneous polynomial solutions of arbitrary degrees, less conservative linear Matrix inequality relaxations can be obtained. Numerical experiments illustrate the better performance and efficiency of the proposed approach when compared to other strategies available in the literature.
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ACC - ℋ ∞ static output feedback control of discrete-time Markov jump linear systems with uncertain Transition Probability Matrix
2014 American Control Conference, 2014Co-Authors: Cecília F. Morais, Márcio F. Braga, Ricardo C. L. F. Oliveira, Pedro L. D. PeresAbstract:This paper investigates the problem of ℋ ∞ static output feedback control design for discrete-time Markov jump linear systems (MJLS), assuming that the Transition Probability Matrix is not precisely known, but affected by different classes of uncertainties: polytopic, bounded or completely unknown elements. All types of uncertainties are modeled through one single representation, expressed in terms of the Cartesian product of simplexes, called multi-simplex. The main novelty of the proposed design procedure is that, differently from previous approaches in the literature, parameter-dependent Lyapunov matrices are used to certify the closed-loop stability with an ℋ ∞ bound for the discrete-time MJLS. The proposed conditions are based on linear Matrix inequality relaxations performed in two steps: the first step generates a parameter-dependent state feedback controller that is employed as an input for the second stage, which synthesizes a robust static output feedback gain assuring an ℋ ∞ guaranteed cost. The proposed strategy can also cope with ℋ ∞ state feedback control for discrete-time MJLS. Numerical examples illustrate the advantages of the proposed methodology when compared to other methods from the literature.
Márcio F. Braga - One of the best experts on this subject based on the ideXlab platform.
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ℋ 2 filter design through multi simplex modeling for discrete time markov jump linear systems with partly unknown Transition Probability Matrix
Conference on Decision and Control, 2014Co-Authors: Cecília F. Morais, Márcio F. Braga, Ricardo C. L. F. Oliveira, Marcio J Lacerda, Pedro L. D. PeresAbstract:This paper is concerned with the ℋ 2 robust filtering problem for discrete-time Markov jump linear systems (MJLS) with Transition Probability Matrix affected by uncertainties. Differently from previous approaches in the literature, the proposed strategy presents a systematic way to handle, simultaneously, different types of uncertainties commonly appearing in the Transition Probability Matrix of MJLS. Fullorder filters with partial, complete or null Markov mode observation are synthesized via a linear Matrix inequality (LMI) based formulation. The main novelty of the proposed filter design procedure is the use of parameter-dependent Lyapunov matrices of arbitrary degree to certify the stochastic stability and to guarantee an upper bound to the ℋ 2 norm of the filtering error system. Moreover, the proposed conditions also include slack variables and scalars. For fixed values of the scalar parameters, the conditions become LMIs. Numerical examples borrowed from the literature illustrate that the proposed filter can provide better ℋ 2 guaranteed costs when compared to other existing methods.
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ℋ∞ static output feedback control of discrete-time Markov jump linear systems with uncertain Transition Probability Matrix
2014 American Control Conference, 2014Co-Authors: Cecília F. Morais, Márcio F. Braga, Ricardo C. L. F. Oliveira, Pedro L. D. PeresAbstract:This paper investigates the problem of ℋ∞ static output feedback control design for discrete-time Markov jump linear systems (MJLS), assuming that the Transition Probability Matrix is not precisely known, but affected by different classes of uncertainties: polytopic, bounded or completely unknown elements. All types of uncertainties are modeled through one single representation, expressed in terms of the Cartesian product of simplexes, called multi-simplex. The main novelty of the proposed design procedure is that, differently from previous approaches in the literature, parameter-dependent Lyapunov matrices are used to certify the closed-loop stability with an ℋ∞ bound for the discrete-time MJLS. The proposed conditions are based on linear Matrix inequality relaxations performed in two steps: the first step generates a parameter-dependent state feedback controller that is employed as an input for the second stage, which synthesizes a robust static output feedback gain assuring an ℋ∞ guaranteed cost. The proposed strategy can also cope with ℋ∞ state feedback control for discrete-time MJLS. Numerical examples illustrate the advantages of the proposed methodology when compared to other methods from the literature.
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CDC - ℋ 2 filter design through multi-simplex modeling for discrete-time Markov jump linear systems with partly unknown Transition Probability Matrix
53rd IEEE Conference on Decision and Control, 2014Co-Authors: Cecília F. Morais, Márcio F. Braga, Ricardo C. L. F. Oliveira, Marcio J Lacerda, Pedro L. D. PeresAbstract:This paper is concerned with the ℋ 2 robust filtering problem for discrete-time Markov jump linear systems (MJLS) with Transition Probability Matrix affected by uncertainties. Differently from previous approaches in the literature, the proposed strategy presents a systematic way to handle, simultaneously, different types of uncertainties commonly appearing in the Transition Probability Matrix of MJLS. Fullorder filters with partial, complete or null Markov mode observation are synthesized via a linear Matrix inequality (LMI) based formulation. The main novelty of the proposed filter design procedure is the use of parameter-dependent Lyapunov matrices of arbitrary degree to certify the stochastic stability and to guarantee an upper bound to the ℋ 2 norm of the filtering error system. Moreover, the proposed conditions also include slack variables and scalars. For fixed values of the scalar parameters, the conditions become LMIs. Numerical examples borrowed from the literature illustrate that the proposed filter can provide better ℋ 2 guaranteed costs when compared to other existing methods.
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***ℋ∞ Filter Design through Multi-simplex Modeling for Discrete-time Markov Jump Linear Systems with Partly Unknown Transition Probability Matrix
IFAC Proceedings Volumes, 2014Co-Authors: Cecília F. Morais, Márcio F. Braga, Ricardo C. L. F. Oliveira, Marcio J Lacerda, Pedro L. D. PeresAbstract:Abstract This paper addresses the problem of *** ℋ ∞ filter design for discrete-time Markov jump linear systems (MJLS) with Transition Probability Matrix affected by uncertainties. The proposed methodology allows to take into account the different types of uncertainties usually adopted in MJLS in a systematic way. New conditions are given for *** ℋ ∞ filter design with partial, complete or null Markov mode availability. Due to the presence of slack variables in the synthesis conditions and to the use of homogeneous polynomial solutions of arbitrary degrees, less conservative linear Matrix inequality relaxations can be obtained. Numerical experiments illustrate the better performance and efficiency of the proposed approach when compared to other strategies available in the literature.
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ACC - ℋ ∞ static output feedback control of discrete-time Markov jump linear systems with uncertain Transition Probability Matrix
2014 American Control Conference, 2014Co-Authors: Cecília F. Morais, Márcio F. Braga, Ricardo C. L. F. Oliveira, Pedro L. D. PeresAbstract:This paper investigates the problem of ℋ ∞ static output feedback control design for discrete-time Markov jump linear systems (MJLS), assuming that the Transition Probability Matrix is not precisely known, but affected by different classes of uncertainties: polytopic, bounded or completely unknown elements. All types of uncertainties are modeled through one single representation, expressed in terms of the Cartesian product of simplexes, called multi-simplex. The main novelty of the proposed design procedure is that, differently from previous approaches in the literature, parameter-dependent Lyapunov matrices are used to certify the closed-loop stability with an ℋ ∞ bound for the discrete-time MJLS. The proposed conditions are based on linear Matrix inequality relaxations performed in two steps: the first step generates a parameter-dependent state feedback controller that is employed as an input for the second stage, which synthesizes a robust static output feedback gain assuring an ℋ ∞ guaranteed cost. The proposed strategy can also cope with ℋ ∞ state feedback control for discrete-time MJLS. Numerical examples illustrate the advantages of the proposed methodology when compared to other methods from the literature.
Wei Feng - One of the best experts on this subject based on the ideXlab platform.
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Robust dissipative filtering for discrete-time Markov jump Lur'e systems with uncertain Transition Probability Matrix
2015 54th IEEE Conference on Decision and Control (CDC), 2015Co-Authors: Yujie Zhang, Yongsheng Ou, Xinyu Wu, Wei FengAbstract:This paper addresses the dissipative filtering problem for a class of Markov jump Lur'e systems with uncertain Transition probabilities in discrete-time domain. The uncertain characteristic of the Transition Probability Matrix is modelled in accordance with the Cartesian product of simplexes, called multi-simplex. A full-order filter is designed such that the resulting error systems are stochastically stable and strictly (Q, S, R)-γ-dissipative. Sufficient conditions for the existence of desired filter are derived in terms of linear Matrix inequalities relaxations. As the main tool we employ a polynomially parameter-dependent Lyapunov function, which depends on the uncertain parameters and the sector condition assumption for the nonlinearities. A numerical example is presented to show the effectiveness of the developed theoretical results.
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CDC - Robust dissipative filtering for discrete-time Markov jump Lur'e systems with uncertain Transition Probability Matrix
2015 54th IEEE Conference on Decision and Control (CDC), 2015Co-Authors: Yujie Zhang, Wei FengAbstract:This paper addresses the dissipative filtering problem for a class of Markov jump Lur'e systems with uncertain Transition probabilities in discrete-time domain. The uncertain characteristic of the Transition Probability Matrix is modelled in accordance with the Cartesian product of simplexes, called multi-simplex. A full-order filter is designed such that the resulting error systems are stochastically stable and strictly (Q, S, R)-γ-dissipative. Sufficient conditions for the existence of desired filter are derived in terms of linear Matrix inequalities relaxations. As the main tool we employ a polynomially parameter-dependent Lyapunov function, which depends on the uncertain parameters and the sector condition assumption for the nonlinearities. A numerical example is presented to show the effectiveness of the developed theoretical results.
Ricardo C. L. F. Oliveira - One of the best experts on this subject based on the ideXlab platform.
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ℋ 2 filter design through multi simplex modeling for discrete time markov jump linear systems with partly unknown Transition Probability Matrix
Conference on Decision and Control, 2014Co-Authors: Cecília F. Morais, Márcio F. Braga, Ricardo C. L. F. Oliveira, Marcio J Lacerda, Pedro L. D. PeresAbstract:This paper is concerned with the ℋ 2 robust filtering problem for discrete-time Markov jump linear systems (MJLS) with Transition Probability Matrix affected by uncertainties. Differently from previous approaches in the literature, the proposed strategy presents a systematic way to handle, simultaneously, different types of uncertainties commonly appearing in the Transition Probability Matrix of MJLS. Fullorder filters with partial, complete or null Markov mode observation are synthesized via a linear Matrix inequality (LMI) based formulation. The main novelty of the proposed filter design procedure is the use of parameter-dependent Lyapunov matrices of arbitrary degree to certify the stochastic stability and to guarantee an upper bound to the ℋ 2 norm of the filtering error system. Moreover, the proposed conditions also include slack variables and scalars. For fixed values of the scalar parameters, the conditions become LMIs. Numerical examples borrowed from the literature illustrate that the proposed filter can provide better ℋ 2 guaranteed costs when compared to other existing methods.
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ℋ∞ static output feedback control of discrete-time Markov jump linear systems with uncertain Transition Probability Matrix
2014 American Control Conference, 2014Co-Authors: Cecília F. Morais, Márcio F. Braga, Ricardo C. L. F. Oliveira, Pedro L. D. PeresAbstract:This paper investigates the problem of ℋ∞ static output feedback control design for discrete-time Markov jump linear systems (MJLS), assuming that the Transition Probability Matrix is not precisely known, but affected by different classes of uncertainties: polytopic, bounded or completely unknown elements. All types of uncertainties are modeled through one single representation, expressed in terms of the Cartesian product of simplexes, called multi-simplex. The main novelty of the proposed design procedure is that, differently from previous approaches in the literature, parameter-dependent Lyapunov matrices are used to certify the closed-loop stability with an ℋ∞ bound for the discrete-time MJLS. The proposed conditions are based on linear Matrix inequality relaxations performed in two steps: the first step generates a parameter-dependent state feedback controller that is employed as an input for the second stage, which synthesizes a robust static output feedback gain assuring an ℋ∞ guaranteed cost. The proposed strategy can also cope with ℋ∞ state feedback control for discrete-time MJLS. Numerical examples illustrate the advantages of the proposed methodology when compared to other methods from the literature.
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CDC - ℋ 2 filter design through multi-simplex modeling for discrete-time Markov jump linear systems with partly unknown Transition Probability Matrix
53rd IEEE Conference on Decision and Control, 2014Co-Authors: Cecília F. Morais, Márcio F. Braga, Ricardo C. L. F. Oliveira, Marcio J Lacerda, Pedro L. D. PeresAbstract:This paper is concerned with the ℋ 2 robust filtering problem for discrete-time Markov jump linear systems (MJLS) with Transition Probability Matrix affected by uncertainties. Differently from previous approaches in the literature, the proposed strategy presents a systematic way to handle, simultaneously, different types of uncertainties commonly appearing in the Transition Probability Matrix of MJLS. Fullorder filters with partial, complete or null Markov mode observation are synthesized via a linear Matrix inequality (LMI) based formulation. The main novelty of the proposed filter design procedure is the use of parameter-dependent Lyapunov matrices of arbitrary degree to certify the stochastic stability and to guarantee an upper bound to the ℋ 2 norm of the filtering error system. Moreover, the proposed conditions also include slack variables and scalars. For fixed values of the scalar parameters, the conditions become LMIs. Numerical examples borrowed from the literature illustrate that the proposed filter can provide better ℋ 2 guaranteed costs when compared to other existing methods.
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***ℋ∞ Filter Design through Multi-simplex Modeling for Discrete-time Markov Jump Linear Systems with Partly Unknown Transition Probability Matrix
IFAC Proceedings Volumes, 2014Co-Authors: Cecília F. Morais, Márcio F. Braga, Ricardo C. L. F. Oliveira, Marcio J Lacerda, Pedro L. D. PeresAbstract:Abstract This paper addresses the problem of *** ℋ ∞ filter design for discrete-time Markov jump linear systems (MJLS) with Transition Probability Matrix affected by uncertainties. The proposed methodology allows to take into account the different types of uncertainties usually adopted in MJLS in a systematic way. New conditions are given for *** ℋ ∞ filter design with partial, complete or null Markov mode availability. Due to the presence of slack variables in the synthesis conditions and to the use of homogeneous polynomial solutions of arbitrary degrees, less conservative linear Matrix inequality relaxations can be obtained. Numerical experiments illustrate the better performance and efficiency of the proposed approach when compared to other strategies available in the literature.
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ACC - ℋ ∞ static output feedback control of discrete-time Markov jump linear systems with uncertain Transition Probability Matrix
2014 American Control Conference, 2014Co-Authors: Cecília F. Morais, Márcio F. Braga, Ricardo C. L. F. Oliveira, Pedro L. D. PeresAbstract:This paper investigates the problem of ℋ ∞ static output feedback control design for discrete-time Markov jump linear systems (MJLS), assuming that the Transition Probability Matrix is not precisely known, but affected by different classes of uncertainties: polytopic, bounded or completely unknown elements. All types of uncertainties are modeled through one single representation, expressed in terms of the Cartesian product of simplexes, called multi-simplex. The main novelty of the proposed design procedure is that, differently from previous approaches in the literature, parameter-dependent Lyapunov matrices are used to certify the closed-loop stability with an ℋ ∞ bound for the discrete-time MJLS. The proposed conditions are based on linear Matrix inequality relaxations performed in two steps: the first step generates a parameter-dependent state feedback controller that is employed as an input for the second stage, which synthesizes a robust static output feedback gain assuring an ℋ ∞ guaranteed cost. The proposed strategy can also cope with ℋ ∞ state feedback control for discrete-time MJLS. Numerical examples illustrate the advantages of the proposed methodology when compared to other methods from the literature.