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Weiming Xiang - One of the best experts on this subject based on the ideXlab platform.
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stability analysis and l1 gain characterization for switched positive systems under Dwell Time constraint
Automatica, 2017Co-Authors: Weiming Xiang, James Lam, Jun ShenAbstract:Abstract This paper deals with the problems of stability analysis and L 1 -gain characterization for continuous-Time switched systems consisting of positive subsystems. With the aid of a discretized copositive Lyapunov function, a sufficient condition ensuring the asymptotic stability of continuous-Time switched positive systems under Dwell-Time constraint is obtained, which can be checked via linear programming. Furthermore, the conservatism of the proposed approach is studied and the result with least conservatism in the framework of discretized copositive Lyapunov function is obtained. The result is then extended to L 1 -gain characterization for switched positive systems. With a prescribed Dwell Time, an unweighted L 1 -gain can be computed via solving a linear programming problem. A numerical example and a practical traffic example are given to illustrate our results.
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ℋ filtering for switched discrete Time systems under asynchronous switching a Dwell Time dependent lyapunov functional method
International Journal of Adaptive Control and Signal Processing, 2015Co-Authors: Weiming Xiang, Jian Xiao, Magdi S MahmoudAbstract:Summary In this article, the filtering problem for switched discrete-Time linear systems under asynchronous switching is addressed in the framework of Dwell Time, where ‘asynchronous switching’ covers more general and practical cases, for example, the switching lags caused by mode identification process are taken into consideration. Firstly, a novel Dwell-Time dependent Lyapunov function (DTDLF) is introduced to solve stability and l2 gain analysis problems. The main advantage of DTDLF approach is that the derived conditions are all convex in system matrices, so it is convenient to be applied into filter design with performance instead of weighted performance as many other previous results. Thus, on the basis of DTLDF, a Dwell-Time dependent filter with Time-varying structure is proposed to achieve the desirable non-weighted filtering performance. It is notable that the proposed approach can also easily characterize the relationships among filtering performance, Dwell Time, and asynchronous Time. Two examples are provided to validate the theoretical findings in this paper. Copyright © 2014 John Wiley & Sons, Ltd.
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on equivalence of two stability criteria for continuous Time switched systems with Dwell Time constraint
Automatica, 2015Co-Authors: Weiming XiangAbstract:In this note, a study on the equivalence of two stability criteria for continuous-Time switched linear systems with Dwell Time constraint is presented. It is demonstrated that, for any Dwell Time satisfying the conditions in stability criterion proposed in Geromel and Colaneri (2006), the conditions in stability criterion of Allerhand and Shaked (2011) also hold as long as the number of decision variables and related LMIs is sufficiently large, which implies the two stability criteria are intrinsically equivalent. The equivalence is obtained by showing that two criteria can be derived from each other with a sufficiently large number of decision variables and LMIs. A numerical example is proposed to illustrate the theoretical results, and an extension to uncertain case is briefly presented.
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stabilization of switched continuous Time systems with all modes unstable via Dwell Time switching
Automatica, 2014Co-Authors: Weiming Xiang, Jian XiaoAbstract:Stabilization of switched systems composed fully of unstable subsystems is one of the most challenging problems in the field of switched systems. In this brief paper, a sufficient condition ensuring the asymptotic stability of switched continuous-Time systems with all modes unstable is proposed. The main idea is to exploit the stabilization property of switching behaviors to compensate the state divergence made by unstable modes. Then, by using a discretized Lyapunov function approach, a computable sufficient condition for switched linear systems is proposed in the framework of Dwell Time; it is shown that the Time intervals between two successive switching instants are required to be confined by a pair of upper and lower bounds to guarantee the asymptotic stability. Based on derived results, an algorithm is proposed to compute the stability region of admissible Dwell Time. A numerical example is proposed to illustrate our approach.
Peng Shi - One of the best experts on this subject based on the ideXlab platform.
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non weighted quasi Time dependent h filtering for switched linear systems with persistent Dwell Time
Automatica, 2015Co-Authors: Lixian Zhang, Songlin Zhuang, Peng ShiAbstract:This paper is concerned with H ∞ filtering for a class of switched linear systems in discrete-Time domain. A more general class of switching signals, the persistent Dwell-Time (PDT) switching is considered rather than the Dwell-Time or average Dwell-Time switching often studied in the literature. The concept on a stage of switching in the type of PDT switching signals is introduced, and each stage consists of a period of persistence and a Dwell-Time portion in which no switching occurs. A proper Lyapunov function suitable to the PDT switching is constructed, which is not only mode-dependent but also quasi-Time-dependent (QTD). Then, a QTD filter is designed such that the resulting filtering error system is globally uniformly asymptotically stable and has a guaranteed H ∞ noise attenuation performance. Certain techniques are explored such that the obtained performance index is of strictly non-weighted H ∞ norm, which contrasts with the weighted (or called exponential) ones, i.e., weaker noise attenuation in the existing literature of switched systems with average Dwell-Time. An example of mass-spring system is provided to show the validity and potential of the developed results.
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stability and stabilization of switched linear systems with mode dependent average Dwell Time
IEEE Transactions on Automatic Control, 2012Co-Authors: Xudong Zhao, Lixian Zhang, Peng Shi, Ming LiuAbstract:In this paper, the stability and stabilization problems for a class of switched linear systems with mode-dependent average Dwell Time (MDADT) are investigated in both continuous-Time and discrete-Time contexts. The proposed switching law is more applicable in practice than the average Dwell Time (ADT) switching in which each mode in the underlying system has its own ADT. The stability criteria for switched systems with MDADT in nonlinear setting are firstly derived, by which the conditions for stability and stabilization for linear systems are also presented. A numerical example is given to show the validity and potential of the developed techniques.
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l_ 2 l_ infty model reduction for switched lpv systems with average Dwell Time
IEEE Transactions on Automatic Control, 2008Co-Authors: Lixian Zhang, Peng ShiAbstract:In this note, the model reduction problem for a class of discrete-Time switched linear parameter varying systems under average Dwell Time switching is investigated. A parameterized reduced-model is constructed and the corresponding existence conditions of such models are derived via strict LMI formulation. The minimal average Dwell Time among all the subsystems and the desired reduced system are obtained such that the resulting model error system is exponentially stable and has a guaranteed l 2-l infin error performance. A numerical example is given to demonstrate the potential and effectiveness of the developed theoretical results.
Lixian Zhang - One of the best experts on this subject based on the ideXlab platform.
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non weighted quasi Time dependent h filtering for switched linear systems with persistent Dwell Time
Automatica, 2015Co-Authors: Lixian Zhang, Songlin Zhuang, Peng ShiAbstract:This paper is concerned with H ∞ filtering for a class of switched linear systems in discrete-Time domain. A more general class of switching signals, the persistent Dwell-Time (PDT) switching is considered rather than the Dwell-Time or average Dwell-Time switching often studied in the literature. The concept on a stage of switching in the type of PDT switching signals is introduced, and each stage consists of a period of persistence and a Dwell-Time portion in which no switching occurs. A proper Lyapunov function suitable to the PDT switching is constructed, which is not only mode-dependent but also quasi-Time-dependent (QTD). Then, a QTD filter is designed such that the resulting filtering error system is globally uniformly asymptotically stable and has a guaranteed H ∞ noise attenuation performance. Certain techniques are explored such that the obtained performance index is of strictly non-weighted H ∞ norm, which contrasts with the weighted (or called exponential) ones, i.e., weaker noise attenuation in the existing literature of switched systems with average Dwell-Time. An example of mass-spring system is provided to show the validity and potential of the developed results.
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stability and stabilization of switched linear systems with mode dependent average Dwell Time
IEEE Transactions on Automatic Control, 2012Co-Authors: Xudong Zhao, Lixian Zhang, Peng Shi, Ming LiuAbstract:In this paper, the stability and stabilization problems for a class of switched linear systems with mode-dependent average Dwell Time (MDADT) are investigated in both continuous-Time and discrete-Time contexts. The proposed switching law is more applicable in practice than the average Dwell Time (ADT) switching in which each mode in the underlying system has its own ADT. The stability criteria for switched systems with MDADT in nonlinear setting are firstly derived, by which the conditions for stability and stabilization for linear systems are also presented. A numerical example is given to show the validity and potential of the developed techniques.
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l_ 2 l_ infty model reduction for switched lpv systems with average Dwell Time
IEEE Transactions on Automatic Control, 2008Co-Authors: Lixian Zhang, Peng ShiAbstract:In this note, the model reduction problem for a class of discrete-Time switched linear parameter varying systems under average Dwell Time switching is investigated. A parameterized reduced-model is constructed and the corresponding existence conditions of such models are derived via strict LMI formulation. The minimal average Dwell Time among all the subsystems and the desired reduced system are obtained such that the resulting model error system is exponentially stable and has a guaranteed l 2-l infin error performance. A numerical example is given to demonstrate the potential and effectiveness of the developed theoretical results.
Masood Dehghan - One of the best experts on this subject based on the ideXlab platform.
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characterization and computation of disturbance invariant sets for constrained switched linear systems with Dwell Time restriction
Automatica, 2012Co-Authors: Masood DehghanAbstract:This paper introduces the concept and characterization of Disturbance-Dwell-Time invariance (DDT-invariance) and Constraint Admissible DDT-invariance (CADDT-invariance) for constrained systems with additive disturbance under Dwell-Time switching. Using the characterization, necessary and sufficient conditions for DDT-invariance and algorithms for the computation of the minimal and maximal constraint admissible convex DDT-invariant sets are provided. Numerical examples of such sets for several systems are also provided.
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brief paper discrete Time switching linear system with constraints characterization and computation of invariant sets under Dwell Time consideration
Automatica, 2012Co-Authors: Masood DehghanAbstract:This paper introduces the concepts of Dwell-Time invariant/contractive (DT-invariant/contractive) set, Constraint Admissible DT-invariant/contractive (CADT-invariant/contractive) set for a discrete-Time switching system under Dwell-Time switching. Main contributions of this paper include a characterization for a DT-contractive set, an algorithm for the computation of the maximal CADT-invariant set, a necessary and sufficient condition for asymptotic stability of the origin of switching systems under Dwell-Time switching and computation of the minimal Dwell-Time needed for asymptotic stability of the origin.
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discrete Time switched linear system with constraints characterization and computation of invariant sets under Dwell Time consideration
Conference on Decision and Control, 2011Co-Authors: Masood Dehghan, Chong Jin Ong, Peter C Y ChenAbstract:This paper introduces the concepts of Dwell-Time invariance (DT-invariance) and maximal constraint admissible DT-invariant set for discrete-Time switching systems under Dwell-Time switching. Main contributions of this paper include a characterization for DT-invariance; a numerical computation of the maximal CADT-invariant set; a necessary and sufficient condition for asymptotic stability of the origin of the switching systems under Dwell Time switching and an algorithm for the computation of the minimal Dwell Time needed for stability.
Patrizio Colaneri - One of the best experts on this subject based on the ideXlab platform.
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a nonconservative lmi condition for stability of switched systems with guaranteed Dwell Time
IEEE Transactions on Automatic Control, 2012Co-Authors: Graziano Chesi, Patrizio Colaneri, J C Geromel, Richard H Middleton, Robert ShortenAbstract:Ensuring stability of switched linear systems with a guaranteed Dwell Time is an important problem in control systems. Several methods have been proposed in the literature to address this problem, but unfortunately they provide sufficient conditions only. This technical note proposes the use of homogeneous polynomial Lyapunov functions in the non-restrictive case where all the subsystems are Hurwitz, showing that a sufficient condition can be provided in terms of an LMI feasibility test by exploiting a key representation of polynomials. Several properties are proved for this condition, in particular that it is also necessary for a sufficiently large degree of these functions. As a result, the proposed condition provides a sequence of upper bounds of the minimum Dwell Time that approximate it arbitrarily well. Some examples illustrate the proposed approach.
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Dwell Time analysis for continuous Time switched linear positive systems
Advances in Computing and Communications, 2010Co-Authors: Annalisa Zappavigna, Patrizio Colaneri, J C Geromel, Robert ShortenAbstract:Dwell Time results are established for a class of switched linear positive systems. Results are also given for a class of Time-delayed switched positive systems. An upper bound to the L 1 -induced norm of switched linear positive systems is computed. Examples are also given to illustrate the efficacy of our results.
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computing upper bounds of the minimum Dwell Time of linear switched systems via homogeneous polynomial lyapunov functions
Advances in Computing and Communications, 2010Co-Authors: Graziano Chesi, Patrizio Colaneri, J C Geromel, Richard H Middleton, Robert ShortenAbstract:This paper investigates the minimum Dwell Time for switched linear systems. It is shown that a sequence of upper bounds of the minimum Dwell Time can be computed by exploiting homogeneous polynomial Lyapunov functions and convex optimization problems based on linear matrix inequalities (LMIs). This sequence is obtained by adopting two possible representations of homogeneous polynomials, one based on Kronecker products, and the other on the square matrix representation (SMR). Some examples illustrate the use and the potentialities of the proposed approach. It is also conjectured that the proposed approach is asymptotically nonconservative, i.e. the exact minimum Dwell Time is obtained by using homogeneous polynomials with sufficiently large degree.
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Dwell Time analysis of deterministic and stochastic switched systems
European Control Conference, 2009Co-Authors: Patrizio ColaneriAbstract:This paper collects a number of recent results on stability and L 2 gain of switched linear systems (both deterministic and stochastic) under a Dwell Time constraint. The switching signal orchestrates the commutations between linear systems (in the deterministic case) or Markov jump linear systems (in the stochastic case). In the latter case, the switching affects both the dynamics of the underlying systems and the associated transition probability matrices. The main focus is on the computation of the minimum Dwell Time ensuring stability and an upper bound of the L 2 gain, in the deterministic case, or stochastic stability (both in the mean square sense and almost sure sense), in the stochastic case. Being the minimum Dwell Time very hardly computable, viable procedures are proposed for a computation of an upper bound through Kronecker calculus, standard H ∞ theory and coupled Lyapunov inequalities.
