Finite Frequency Approach for H∞ model reduction of 2D continuous systems
01 Jul 2019-pp 177-182
TL;DR: Using the well known generalized Kalman Yakubovich Popov Lemma and the Finsler's Lemma, sufficient conditions for the existence of H∞ model reduction for different FF ranges are proposed and then unified in terms of solving a set of linear matrix inequalities (LMIs).
Abstract: This paper considers the problem of H∞ model reduction problem with finite frequency (FF) ranges of the input vector for two-dimensional (2D) continuous systems. Given an asymptotically stable system, the main objective is to find a stable reduced-order model such that the error of the transfer functions between the original system and the reduced-order one is bounded over a FF range. Using the well known generalized Kalman Yakubovich Popov (gKYP) Lemma and the Finsler's Lemma, sufficient conditions for the existence of H∞ model reduction for different FF ranges are proposed and then unified in terms of solving a set of linear matrix inequalities (LMIs). Finally, the effectiveness of the proposed method is illustrated by a numerical example.
Citations
More filters
01 Apr 2020
TL;DR: In this paper, the performance of the descriptor system with continuous-time was studied and the sufficient condition was given in form of strict LMI for the problem that such descriptor systems are admissible with disturbance attenuation level.
Abstract: In this paper, we study $H_{\infty}$ performance for the descriptor systems with continuous-time. By using Finsler’s lemma technique and LMI approach, the sufficient condition is given in form of strict LMI for the problem that such descriptor systems are admissible with $H_{\infty}$ disturbance attenuation level. Finally, a numerical examples are given to validate our results.
1 citations
Cites methods from "Finite Frequency Approach for H∞ mo..."
...To mention a few, stability analysis and stabilization of 1D discrte and continuous systems were studied in [8], [10]; H2 or H∞ controllers and filter were designed in [6], [7], [9], [18], [20], [22], [27]; H∞ model reduction are addressed in [12]–[14], [17], [19], [21]; H∞ controllers and filters for 2D linear and nolinear systems were given in [16], [24]– [26]; analysis and design of H∞ controllers for 2D singular systems with selays is addressed in [23]; stability analysis of positive descriptor systems is given in [15]....
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01 Apr 2020
TL;DR: A new design sufficient condition via linear matrix Inequality (LMIs) formulations is proposed, ensuring that the error system is stable and has a minimized $H_{\infty}$ performance when frequency ranges of noises are known beforehand.
Abstract: This paper deals with the problem of $H_{\infty}$ filtering for T-S fuzzy continuous-time systems in low frequency $(LF)$ doamin. The objective is to propose a new design sufficient condition via linear matrix Inequality (LMIs) formulations, ensuring that the error system is stable and has a minimized $H_{\infty}$ performance when frequency ranges of noises are known beforehand. Less conservative results are obtained by using the new low frequency (LF)$H_{\infty}$ performance index is firstly defined, projection lemma and some independent matrices. Simulation example demonstrate the technique and its advantage.
Cites background from "Finite Frequency Approach for H∞ mo..."
...In recent years, there has been a growing interest in the finite frequency, such as H∞ filtering for T-S fuzzy systems (see [14] [15] [16] [27] and the references therein), uncertain systems [10] [11] [23], H∞ control in [25], and model reduction problem [22] [24] [26]....
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21 Oct 2020
TL;DR: In this paper, the authors considered the finite frequency (FF) and $H ∞$ model reduction for two dimensional (2D) discrete Takagi-Sugeno (TS) fuzzy Roesser models.
Abstract: In this work, we considers the finite frequency (FF) and $H_{\infty}$ model reduction for two dimensional (2D) discrete Takagi-Sugeno (TS) fuzzy Roesser models. The problem to be solved in the work is to find a reduced order model such that to approximate the original system with comparatively small. Moreover, as an the application of the developed generalized Kalman Yakubovich Popov (gKYP) lemma based on the proposed linear matrix inequality (LMI), new design conditions guaranteeing the $H_{\infty}$ performance. Finally, a practical example is given to show that the developed FF distributed model reduction design method has less conservation than the method for the entire frequency region.
Cites background from "Finite Frequency Approach for H∞ mo..."
...To mention a few, For the 2D linear case ( see, [21]–[23], [25], [28])....
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13 Jul 2005
TL;DR: This paper presents SVD-Krylov Methods and Case Studies, a monograph on model reduction using Krylov methods for linear dynamical systems, and some examples of such reduction schemes.
Abstract: Preface Part I. Introduction: 1. Introduction 2. Motivating examples Part II. Preliminaries: 3. Tools from matrix theory 4. Linear dynamical systems, Part 1 5. Linear dynamical systems, Part 2 6. Sylvester and Lyapunov equations Part III. SVD-based Approximation Methods: 7. Balancing and balanced approximations 8. Hankel-norm approximation 9. Special topics in SVD-based approximation methods Part IV. Krylov-based Approximation Methods: 10. Eigenvalue computations 11. Model reduction using Krylov methods Part V. SVD-Krylov Methods and Case Studies: 12. SVD-Krylov methods 13. Case studies 14. Epilogue 15. Problems Bibliography Index.
2,893 citations
"Finite Frequency Approach for H∞ mo..." refers background in this paper
...In addition, the model reduction is one of the fundamental problems in the field of control theory, which has been extensively investigated in the past several decades [9][10]....
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TL;DR: In this paper, the linear time-discrete state-space model is generalized from single-dimensional time to two-dimensional space, which includes extending certain basic known concepts from one to two dimensions, such as the general response formula, state transition matrix, Cayley-Hamilton theorem, observability, and controllability.
Abstract: The linear time-discrete state-space model is generalized from single-dimensional time to two-dimensional space. The generalization includes extending certain basic known concepts from one to two dimensions. These concepts include the general response formula, state-transition matrix, Cayley-Hamilton theorem, observability, and controllability.
1,710 citations
"Finite Frequency Approach for H∞ mo..." refers background in this paper
...It is known that many practical processes can be mathematically modeled as by two-dimensional (2D) systems, such as image data processing, transmission, gas absorption and thermal processes, water stream heating, planar circuits and signal filtering [1] [2] [3]....
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TL;DR: In this article, a survey of balancing related model reduction methods and their corresponding error norms is presented, and also some new results are introduced, including a modified positive real balancing scheme with an absolute error bound.
Abstract: Balanced truncation is one of the most common model reduction schemes. In this note, we present a survey of balancing related model reduction methods and their corresponding error norms, and also introduce some new results. Five balancing methods are studied: (1) Lyapunov balancing, (2) stochastic balancing, (3) bounded real balancing, (4) positive real balancing and (5) frequency weighted balancing. For positive real balancing, we introduce a multiplicative-type error bound. Moreover, for a certain subclass of positive real systems, a modified positive-real balancing scheme with an absolute error bound is proposed. We also develop a new frequency-weighted balanced reduction method with a simple bound on the error system based on the frequency domain representations of the system gramians. Two numerical examples are illustrated to verify the efficiency of the proposed methods.
773 citations
"Finite Frequency Approach for H∞ mo..." refers background in this paper
...In addition, the model reduction is one of the fundamental problems in the field of control theory, which has been extensively investigated in the past several decades [9][10]....
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