Stability and Stabilization of 2D Singular Systems: A Strict LMI Approach

This paper deals with the stability and stabilization of 2D singular systems described by a Roesser model. The proposed results are presented in terms of a strict linear matrix inequality (LMI), which makes possible to elaborate a new sufficient admissibility condition. The design of a state feedback controller is then treated using this condition, deriving a sufficient condition for the admissibility of the closed-loop system. A numerical example is given at the end of the paper, which illustrates the effectiveness of the proposed methodology.

[1]  Zhengrong Xiang,et al.  Stability Analysis and Stabilization of Discrete-Time 2D Switched Systems , 2012, Circuits, Systems, and Signal Processing.

[2]  Yun Zou,et al.  H ∞ control for 2-D singular delayed systems , 2011, Int. J. Syst. Sci..

[3]  Manish Tiwari,et al.  A Survey on the Stability of 2-D Discrete Systems Described by Fornasini-Marchesini Second Model , 2012 .

[4]  Shengyuan Xu,et al.  Robust stability and stabilisation of 2D discrete state-delayed systems , 2004, Syst. Control. Lett..

[5]  A. Michel,et al.  Stability analysis of state-space realizations for two-dimensional filters with overflow nonlinearities , 1994 .

[6]  K. Galkowski,et al.  LMI approach to state-feedback stabilization of multidimensional systems , 2003 .

[7]  T. Hinamoto.  Stability of 2-D discrete systems described by the Fornasini-Marchesini second model , 1997 .

[8]  Shengyuan Xu,et al.  H∞ model reduction for discrete-time singular systems , 2003, Syst. Control. Lett..

[9]  G. Duan.  Analysis and Design of Descriptor Linear Systems , 2010 .

[10]  T. Kaczorek.  Two-Dimensional Linear Systems , 1985 .

[11]  Hamid Reza Shaker,et al.  Lyapunov stability for continuous-time multidimensional nonlinear systems , 2014 .

[13]  Yun Zou,et al.  The Jump Behavior and Stability Analysis for 2-D Singular Systems , 2000, Multidimens. Syst. Signal Process..

[14]  Krzysztof Galkowski,et al.  A Perspective on Singularity in 2D Linear Systems , 2000, Multidimens. Syst. Signal Process..

[15]  Derong Liu,et al.  Lyapunov stability of two-dimensional digital filters with overflow nonlinearities , 1998 .

[16]  Yun Zou,et al.  Stability for two-dimensional singular discrete systems described by general model , 2008, Multidimens. Syst. Signal Process..

[17]  Olivier Bachelier,et al.  Exponential stability conditions for 2D continuous state-delayed systems , 2011, The 2011 International Workshop on Multidimensional (nD) Systems.

[18]  Yun Zou,et al.  Duality of 2-D singular systems of Roesser models , 2007 .

[19]  Mohamed Chaabane,et al.  Stability of 2D Discrete Takagi–Sugeno Systems , 2017, Circuits Syst. Signal Process..

[20]  Olivier Bachelier,et al.  Stability and stabilization of 2D continuous state-delayed systems , 2011, IEEE Conference on Decision and Control and European Control Conference.

[21]  Shengyuan Xu,et al.  Bounded real lemma and robust Hinfinity control of 2-D singular Roesser models , 2005, Syst. Control. Lett..

[22]  Weiqun Wang,et al.  Delay-dependent stability for 2-D singular systems with state-varying delay in Roesser model: An LMI approach , 2014, CCC 2014.

[23]  Abdelaziz Hmamed,et al.  Robust H∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_{\infty }$$\end{document} Filtering for Uncertain 2D Singul , 2015, Circuits, Systems, and Signal Processing.

[24]  Mansour Souissi,et al.  Stability and stabilization of continuous descriptor systems: An LMI approach , 2006 .

[25]  Karolos M. Grigoriadis,et al.  A unified algebraic approach to linear control design , 1998 .

[26]  Shyh-Feng Chen,et al.  Stability analysis and stabilization of 2-D singular Roesser models , 2012, 2012 7th IEEE Conference on Industrial Electronics and Applications (ICIEA).

[27]  Andreas Antoniou,et al.  Two-Dimensional Digital Filters , 2020 .

[28]  D. Mehdi,et al.  Admissibility and state feedback admissibilization of discrete singular systems : An LMI approach , 2008, 2008 16th Mediterranean Conference on Control and Automation.

[29]  Krzysztof Galkowski,et al.  On the connection between discrete linear repetitive processes and 2-D discrete linear systems , 2017, Multidimens. Syst. Signal Process..

[30]  Yun Zou,et al.  A Note on the Internal Stability for 2-D Singular Discrete Systems , 2004, Multidimens. Syst. Signal Process..

[31]  Mansour Souissi,et al.  Robust Admissibilization of Descriptor Systems by Static Output-Feedback: An LMI Approach , 2011 .