Relaxed global asymptotic stability of 2-D state-space digital filters described by Roesser model with polytopic-type uncertainty

The problem of stability analysis of 2-D state-space digital filters described by Roesser model with parameter uncertainty is addressed in this paper. The underlying parameter uncertainty is modeled by a convex bounded (polytope type) uncertain domain. By applying both a new parameter-dependent Lyapunov function and a kind of matrix transformation technique, relaxed global asymptotic stability criteria of the 2-D state-space digital filters are proposed in terms of linear matrix inequalities (LMIs), which can be easily solved via standard numerical software. More importantly, the conservatism of the obtained global asymptotic stability criteria could be significantly reduced than existing ones. Finally, a numerical example is provided to illustrate the effectiveness of the proposed approach.

[1]  Huijun Gao,et al.  Robust finite frequency Hinfinity filtering for uncertain 2-D Roesser systems , 2012, Autom..

[2]  Priyanka Kokil,et al.  Stability of 2-D digital filters described by the Roesser model using any combination of quantization and overflow nonlinearities , 2012, Signal Process..

[3]  Huijun Gao,et al.  Novel Robust Stability Criteria for Stochastic Hopfield Neural Networks With Time Delays , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[4]  R. Jackson Inequalities , 2007, Algebra for Parents.

[5]  Vimal Singh New LMI condition for the nonexistence of overflow oscillations in 2-D state-space digital filters using saturation arithmetic , 2007, Digit. Signal Process..

[6]  G. Marchesini,et al.  State-space realization theory of two-dimensional filters , 1976 .

[7]  Yong He,et al.  OPTIMAL REPETITIVE CONTROL BASED ON TWO-DIMENSIONAL MODEL , 2012 .

[8]  Krzysztof Galkowski,et al.  PI control of discrete linear repetitive processes , 2006, Autom..

[9]  Eric Rogers,et al.  Output-feedback control of discrete linear repetitive processes , 1993 .

[10]  Huijun Gao,et al.  A new design of robust H2 filters for uncertain systems , 2008, Syst. Control. Lett..

[11]  Vimal Singh New approach to stability of 2-D discrete systems with state saturation , 2012, Signal Process..

[12]  Haranath Kar,et al.  Robust stability of 2-D discrete systems employing generalized overflow nonlinearities: An LMI approach , 2011, Digit. Signal Process..

[13]  R. Roesser A discrete state-space model for linear image processing , 1975 .

[14]  Eric Rogers,et al.  Analysis of Linear Iterative Learning Control Schemes - A 2D Systems/Repetitive Processes Approach , 2000, Multidimens. Syst. Signal Process..

[15]  Wei Xing Zheng,et al.  Reduced-order H2 filtering for discrete linear repetitive processes , 2011, Signal Process..

[16]  Vimal Singh Improved LMI-based criterion for global asymptotic stability of 2-D state-space digital filters described by Roesser model using two's complement arithmetic , 2012, Digit. Signal Process..

[17]  Guo-Ping Liu,et al.  Filtering for Discrete-Time Networked Nonlinear Systems With Mixed Random Delays and Packet Dropouts , 2011, IEEE Transactions on Automatic Control.

[18]  Haranath Kar A new criterion for the global asymptotic stability of 2-D state-space digital filters with two's complement overflow arithmetic , 2012, Signal Process..

[19]  Abdellah Benzaouia,et al.  STATE-FEEDBACK STABILIZATION OF 2 D CONTINUOUS SYSTEMS WITH DELAYS , 2022 .

[20]  Krzysztof Galkowski,et al.  LMI based output feedback control of discrete linear repetitive processes , 2004, Proceedings of the 2004 American Control Conference.

[21]  Ligang Wu,et al.  Mixed H2/H∞ approach to fault detection of discrete linear repetitive processes , 2011, J. Frankl. Inst..

[22]  Vimal Singh,et al.  2-D digital filter realization without overflow oscillations , 2013 .

[23]  Haranath Kar A novel criterion for the global asymptotic stability of 2-D discrete systems described by Roesser model using saturation arithmetic , 2010, Digit. Signal Process..

[24]  Wei Xing Zheng,et al.  Generalized H2 fault detection for two-dimensional Markovian jump systems , 2012, Autom..

[25]  Huijun Gao,et al.  A Parameter-Dependent Approach to Robust $H_{\infty }$ Filtering for Time-Delay Systems , 2008, IEEE Transactions on Automatic Control.

[26]  Thierry-Marie Guerra,et al.  LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in the Takagi-Sugeno's form , 2004, Autom..

[27]  Haranath Kar A new sufficient condition for the global asymptotic stability of 2-D state-space digital filters with saturation arithmetic , 2008, Signal Process..

[28]  Huijun Gao,et al.  Filtering for uncertain 2-D discrete systems with state delays , 2007, Signal Process..

[29]  Xiangpeng Xie,et al.  Control Synthesis of Discrete-Time T–S Fuzzy Systems Based on a Novel Non-PDC Control Scheme , 2013, IEEE Transactions on Fuzzy Systems.

[30]  Huijun Gao,et al.  I filtering for 2D Markovian jump systems , 2008, Autom..

[31]  Ligang Wu,et al.  Sliding mode control of two-dimensional systems in Roesser model , 2008 .

[32]  Vimal Singh,et al.  Stability analysis of 2-D state-space digital filters using Lyapunov function: a caution , 1997, IEEE Trans. Signal Process..