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Victor Sreeram - One of the best experts on this subject based on the ideXlab platform.
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Frequency interval model reduction of complex fir digital filters
Numerical Algebra Control and Optimization, 2019Co-Authors: Ahmad Jazlan, Umair Zulfiqar, Victor Sreeram, Roberto Togneri, Deepak Kumar, Hasan Firdaus Mohd ZakiAbstract:In this paper, a model reduction method for FIR filters with complex coefficients based on frequency interval impulse response Gramians is developed. The advantage of the proposed method is that only one Lyapunov equation needs to be solved in order to obtain the information regarding the frequency interval controllability and observability of the system. In addition this method overcomes the limitations of using cross Gramians which are not applicable for filters with complex coefficients. The effectiveness of the proposed method is demonstrated by a numerical example.
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Model Reduction Using Parameterized Limited Frequency Interval Gramians for 1-D and 2-D Separable Denominator Discrete-Time Systems
IEEE Transactions on Circuits and Systems I: Regular Papers, 2018Co-Authors: Deepak Kumar, Victor Sreeram, Xin DuAbstract:In this paper, we propose model reduction algorithms based on the frequency-domain interval Gramians for 1-D and separable denominator 2-D discrete-time systems using balanced truncation as a parameterized combination of unweighted and the limited-frequency interval Gramians. The values of free parameters are computed using a line search optimization. The proposed algorithms provide a substantial improvement in the approximation error than the well-known existing techniques and generate stable reduced models along with an easily computable error-bound. The effectiveness of proposed algorithms is validated with the help of numerical examples of a sixth-order elliptic low-pass filter and a (6, 6)-order Roesser model of a separable denominator 2-D system.
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frequency interval cross gramians for linear and bilinear systems
Asian Journal of Control, 2017Co-Authors: Hamid Reza Shaker, Ahmad Jazlan, Victor Sreeram, Roberto Togneri, Ha Binh MinhAbstract:In many control engineering problems, it is desired to analyze the systems at particular frequency intervals of interest. This paper focuses on the development of frequency interval cross gramians for both linear and bilinear systems. New generalized Sylvester equations for calculating the frequency interval cross gramians are derived in order to be used to obtain information regarding controllability and observability within a single matrix. The advantage of the proposed method is that it is computationally more efficient compared to existing gramian-based techniques since only half of the number of equations need to be solved in order to obtain information regarding the controllability and observability of a system compared to existing techniques. Numerical examples are provided to demonstrate the computational efficiency of the proposed method which uses frequency interval cross gramians relative to existing methods.
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AuCC - Generalized gramian based frequency interval model reduction for unstable systems
2016 Australian Control Conference (AuCC), 2016Co-Authors: Ahmad Jazlan, Victor Sreeram, Roberto Togneri, Ha Binh MinhAbstract:Frequency interval controllability and observability gramian matrices are important in order to understand the characteristics of systems which are inherently frequency dependent. Obtaining these frequency interval controllability and observability gramian matrices requires solving a pair of Lyapunov equations. However for certain systems these Lyapunov equations are not solvable. In addition the eigenvalues of the product of the frequency interval controllability and observability gramians may also be complex numbers and therefore these gramians are not applicable to used in the context of model reduction. To overcome these issues, generalized frequency interval controllability and observability gramians are introduced in this paper and the applicability of these generalized gramians to be used in model reduction is demonstrated.
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Frequency interval balanced truncation of discrete-time bilinear systems
Cogent engineering, 2016Co-Authors: Ahmad Jazlan, Hamid Reza Shaker, Victor Sreeram, Roberto TogneriAbstract:This paper presents the development of a new model reduction method for discrete-time bilinear systems based on the balanced truncation framework. In many model reduction applications, it is advantageous to analyze the characteristics of the system with emphasis on particular frequency intervals of interest. In order to analyze the degree of controllability and observability of discrete-time bilinear systems with emphasis on particular frequency intervals of interest, new generalized frequency interval controllability and observability gramians are introduced in this paper. These gramians are the solution to a pair of new generalized Lyapunov equations. The conditions for solvability of these new generalized Lyapunov equations are derived and a numerical solution method for solving these generalized Lyapunov equations is presented. Numerical examples which illustrate the usage of the new generalized frequency interval controllability and observability gramians as part of the balanced truncation framework ...
Hamid Reza Shaker - One of the best experts on this subject based on the ideXlab platform.
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CDC - Generalized frequency-interval balanced model reduction method
52nd IEEE Conference on Decision and Control, 2020Co-Authors: Hamid Reza ShakerAbstract:In this paper, a new method for model reduction of bilinear systems is presented. The method is developed in particular for many applications in which one is interested to approximate a system in a given frequency-interval. To this end, new generalized frequency-interval gramians are introduced for bilinear systems. It is shown that these gramians are the solutions to the so-called frequency-interval generalized Lyapunov equations. Algorithms are proposed to solve such equations iteratively. The method is further illustrated with the help of an illustrative example. The numerical results show that the method is more accurate than its previous counterpart which is based on the ordinary gramians.
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On the existence of frequency-interval gramians for bilinear systems
European Journal of Control, 2017Co-Authors: Hamid Reza Shaker, Maryamsadat TahavoriAbstract:Abstract It is well-known that gramians are specific matrices which show the degree of controllability and observability. Therefore gramians are very popular in applications such as model reduction and control configuration selection. The frequency-interval controllability and observability gramians have been recently introduced for bilinear systems as the solutions to the generalized frequency-interval Lyapunov equations. Analogous to ordinary gramians for bilinear systems, it might happen that the frequency-interval Lyapunov equations have unique solutions which are not controllability and observability gramians of the bilinear systems. In other words, solvability of the frequency-interval Lyapunov equations does not guarantee the existence of the frequency-interval gramians. In this paper, the conditions which are required for the existence of frequency-interval gramians are obtained. Further, to cope with the problem of the existence of gramians, a scaling-based method is proposed. A proof for the theorem which suggests an iterative scheme for computing the frequency-interval generalized gramians is also presented in this paper.
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frequency interval cross gramians for linear and bilinear systems
Asian Journal of Control, 2017Co-Authors: Hamid Reza Shaker, Ahmad Jazlan, Victor Sreeram, Roberto Togneri, Ha Binh MinhAbstract:In many control engineering problems, it is desired to analyze the systems at particular frequency intervals of interest. This paper focuses on the development of frequency interval cross gramians for both linear and bilinear systems. New generalized Sylvester equations for calculating the frequency interval cross gramians are derived in order to be used to obtain information regarding controllability and observability within a single matrix. The advantage of the proposed method is that it is computationally more efficient compared to existing gramian-based techniques since only half of the number of equations need to be solved in order to obtain information regarding the controllability and observability of a system compared to existing techniques. Numerical examples are provided to demonstrate the computational efficiency of the proposed method which uses frequency interval cross gramians relative to existing methods.
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Frequency interval balanced truncation of discrete-time bilinear systems
Cogent engineering, 2016Co-Authors: Ahmad Jazlan, Hamid Reza Shaker, Victor Sreeram, Roberto TogneriAbstract:This paper presents the development of a new model reduction method for discrete-time bilinear systems based on the balanced truncation framework. In many model reduction applications, it is advantageous to analyze the characteristics of the system with emphasis on particular frequency intervals of interest. In order to analyze the degree of controllability and observability of discrete-time bilinear systems with emphasis on particular frequency intervals of interest, new generalized frequency interval controllability and observability gramians are introduced in this paper. These gramians are the solution to a pair of new generalized Lyapunov equations. The conditions for solvability of these new generalized Lyapunov equations are derived and a numerical solution method for solving these generalized Lyapunov equations is presented. Numerical examples which illustrate the usage of the new generalized frequency interval controllability and observability gramians as part of the balanced truncation framework ...
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Frequency-Interval Model Reduction of Bilinear Systems
IEEE Transactions on Automatic Control, 2014Co-Authors: Hamid Reza Shaker, Maryamsadat TahavoriAbstract:In this technical note, a new method for model reduction of bilinear systems is presented. The method is developed in particular for many applications in which one is interested to approximate a system in a given frequency-interval. To this end, new generalized frequency-interval gramians are introduced for bilinear systems. It is shown that these gramians are the solutions to the so-called frequency-interval generalized Lyapunov equations. The conditions for these equations to be solvable are derived and an algorithm is proposed to solve such equations iteratively. The method is further illustrated with the help of an illustrative example. The numerical results show that the method is more accurate than its previous counterpart which is based on the ordinary gramians.
Maryamsadat Tahavori - One of the best experts on this subject based on the ideXlab platform.
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On the existence of frequency-interval gramians for bilinear systems
European Journal of Control, 2017Co-Authors: Hamid Reza Shaker, Maryamsadat TahavoriAbstract:Abstract It is well-known that gramians are specific matrices which show the degree of controllability and observability. Therefore gramians are very popular in applications such as model reduction and control configuration selection. The frequency-interval controllability and observability gramians have been recently introduced for bilinear systems as the solutions to the generalized frequency-interval Lyapunov equations. Analogous to ordinary gramians for bilinear systems, it might happen that the frequency-interval Lyapunov equations have unique solutions which are not controllability and observability gramians of the bilinear systems. In other words, solvability of the frequency-interval Lyapunov equations does not guarantee the existence of the frequency-interval gramians. In this paper, the conditions which are required for the existence of frequency-interval gramians are obtained. Further, to cope with the problem of the existence of gramians, a scaling-based method is proposed. A proof for the theorem which suggests an iterative scheme for computing the frequency-interval generalized gramians is also presented in this paper.
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Frequency-Interval Model Reduction of Bilinear Systems
IEEE Transactions on Automatic Control, 2014Co-Authors: Hamid Reza Shaker, Maryamsadat TahavoriAbstract:In this technical note, a new method for model reduction of bilinear systems is presented. The method is developed in particular for many applications in which one is interested to approximate a system in a given frequency-interval. To this end, new generalized frequency-interval gramians are introduced for bilinear systems. It is shown that these gramians are the solutions to the so-called frequency-interval generalized Lyapunov equations. The conditions for these equations to be solvable are derived and an algorithm is proposed to solve such equations iteratively. The method is further illustrated with the help of an illustrative example. The numerical results show that the method is more accurate than its previous counterpart which is based on the ordinary gramians.
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frequency interval control configuration selection for multivariable bilinear systems
Journal of Process Control, 2013Co-Authors: Hamid Reza Shaker, Maryamsadat TahavoriAbstract:Abstract Control configuration selection is the procedure of choosing the appropriate input and output pairs for the design of decoupled (SISO or block) controllers for multivariable systems. This step is an important prerequisite for a successful industrial control strategy. The focus of this paper is on the problem of control configuration selection for a class of nonlinear systems which is known as bilinear systems. First, new frequency-interval gramians are presented for bilinear systems. These gramians are devised in particular for many applications in which one is interested in analysis and control of a system within a frequency-interval. It is shown that these gramians are the solutions to the so-called frequency-interval generalized Lyapunov equations. These gramians are used in the interaction measure for control configuration selection of MIMO bilinear systems. Most of the results on control configuration selection, which have been proposed so far, can only support linear systems. The proposed gramian-based interaction measure supports bilinear processes, can show the input–output interactions for any frequency-interval of interest, and can be used to propose a richer sparse or block diagonal controller structure.
Muhammad Imran - One of the best experts on this subject based on the ideXlab platform.
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a frequency limited interval gramians based model reduction technique with error bounds
Circuits Systems and Signal Processing, 2015Co-Authors: Muhammad Imran, Abdul GhafoorAbstract:A balanced model reduction technique that is based on frequency limited interval Gramians is proposed. The technique provides stable models and also yields frequency response error bounds. Numerical examples are also presented. The results are comparable with other frequency limited interval Gramians-based model reduction techniques.
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Limited frequency interval Gramian-based model reduction for generalised non-singular discrete time systems
IET Control Theory & Applications, 2015Co-Authors: Muhammad Imran, Abdul Ghafoor, Victor SreeramAbstract:A limited frequency interval Gramians-based model reduction technique for generalised non-singular discrete time systems is presented. The technique generalises the results of existing limited frequency interval Gramians-based model reduction (of discrete time systems) schemes to general non-singular discrete time systems. Numerical examples are also presented to illustrate the proposed technique.
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AuCC - Limited frequency interval Gramians based model reduction for nonsingular generalized systems
2013 Australian Control Conference, 2013Co-Authors: Muhammad Imran, Safia Akram, Abdul Ghafoor, Victor SreeramAbstract:Limited frequency interval Gramians based model reduction technique for generalized nonsingular systems is presented. The technique extends results of existing limited frequency interval Gramians schemes for standard systems. Numerical examples are also included.
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Limited frequency interval Gramians based model reduction for nonsingular generalized systems
2013 Australian Control Conference, 2013Co-Authors: Muhammad Imran, Safia Akram, Abdul Ghafoor, Victor SreeramAbstract:Limited frequency interval Gramians based model reduction technique for generalized nonsingular systems is presented. The technique extends results of existing limited frequency interval Gramians schemes for standard systems. Numerical examples are also included.
H. Toda - One of the best experts on this subject based on the ideXlab platform.
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Design of 2‐D separable‐denominator digital filters using impulse response Grammians
Electronics and Communications in Japan Part Iii-fundamental Electronic Science, 1991Co-Authors: T. Hinamoto, H. Toda, Ryuji YamaguchiAbstract:A technique is developed for designing 2-D separable-denominator digital filters in the spatial domain. First, a given 2-D FIR digital filter is realized in a canonic form by the Roesser model whose transfer function is separable in the denominator. Then, the reduced-order model is obtained using eigenvalue-eigenvector decomposition on the impulse response Grammians derived from the realization. The proposed technique utilizes the impulse response Grammians considered here for 2-D separable-denominator digital filters, which are extensions of those proposed for single-input/single-output 1-D linear systems. The stability of the resulting filter is always guaranteed. Finally, two numerical examples are given to illustrate the utility of the proposed technique.
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The use of impulse response Grammians in the design of 2-D separable-denominator digital filters
[Proceedings] ICASSP 91: 1991 International Conference on Acoustics Speech and Signal Processing, 1991Co-Authors: T. Hinamoto, H. TodaAbstract:A technique is developed for designing two-dimensional (2-D) separable-denominator digital filters in the spatial domain. The proposed technique utilizes the impulse response Grammians considered for 2-D separable-denominator digital filters. These Grammians are extensions of that proposed for single-input/single-output 1-D linear systems. The stability of the resulting filter is always guaranteed. Finally, an example is given to illustrate the use of the proposed technique.
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design of 2 d separable denominator digital filters using impulse response Grammians
Electronics and Communications in Japan Part Iii-fundamental Electronic Science, 1991Co-Authors: T. Hinamoto, H. Toda, Ryuji YamaguchiAbstract:A technique is developed for designing 2-D separable-denominator digital filters in the spatial domain. First, a given 2-D FIR digital filter is realized in a canonic form by the Roesser model whose transfer function is separable in the denominator. Then, the reduced-order model is obtained using eigenvalue-eigenvector decomposition on the impulse response Grammians derived from the realization. The proposed technique utilizes the impulse response Grammians considered here for 2-D separable-denominator digital filters, which are extensions of those proposed for single-input/single-output 1-D linear systems. The stability of the resulting filter is always guaranteed. Finally, two numerical examples are given to illustrate the utility of the proposed technique.
