An extension of Sliding Mode Control design for the 2-D systems in Roesser Model

This letter introduces a strategy design of Sliding Mode Control (SMC) for Two-Dimensional (2-D) systems. The dynamic updating of the 2-D system is considered as a Roesser Model (RM). The proposed method consists of two stages, switching surface design and control law design. Moreover, the robustness of the proposed method for an uncertain system has been investigated. Simulation results verify the efficiency of this approach.

[1]  R. Decarlo,et al.  Variable structure control of nonlinear multivariable systems: a tutorial , 1988, Proc. IEEE.

[2]  D. H. Owens,et al.  Iterative learning control — 2D control systems from theory to application , 2004 .

[3]  Christopher Edwards,et al.  Discrete output feedback sliding-mode control with integral action , 2006 .

[4]  Brian D. O. Anderson,et al.  Stability and the matrix Lyapunov equation for discrete 2-dimensional systems , 1986 .

[5]  Cishen Zhang,et al.  Hinfinity control and robust stabilization of two-dimensional systems in Roesser models , 2001, Autom..

[6]  Vimal Singh.  On global asymptotic stability of 2-D discrete systems with state saturation , 2008 .

[7]  Yaodong Pan,et al.  Variable structure control with sliding sector , 2000, Autom..

[8]  Jan Wikander,et al.  Model reference discrete-time sliding mode control of linear motor precision servo systems , 2004 .

[9]  Jean-Jacques E. Slotine,et al.  Robot analysis and control , 1988, Autom..

[10]  Tamal Bose.  Asymptotic stability of two-dimensional digital filters under quantization , 1994, IEEE Trans. Signal Process..

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

[12]  John Y. Hung,et al.  Variable structure control: a survey , 1993, IEEE Trans. Ind. Electron..

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

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

[15]  Vadim I. Utkin,et al.  A control engineer's guide to sliding mode control , 1999, IEEE Trans. Control. Syst. Technol..

[16]  Changyun Wen,et al.  Adaptive control of a class of 2-D discrete systems , 2003 .

[17]  Jeongho Cho,et al.  Quasi-sliding mode control strategy based on multiple-linear models , 2007, Neurocomputing.

[18]  Haranath Kar,et al.  Optimal guaranteed cost control of 2-D discrete uncertain systems: An LMI approach , 2007, Signal Process..

[19]  V. Utkin.  Variable structure systems with sliding modes , 1977 .

[20]  A. Keyhani,et al.  Sensorless Sliding-Mode Control of Induction Motors Using Operating Condition Dependent Models , 2002, IEEE Power Engineering Review.

[21]  Weibing Gao,et al.  Discrete-time variable structure control systems , 1995, IEEE Trans. Ind. Electron..

[22]  T. Hinamoto.  2-D Lyapunov equation and filter design based on the Fornasini-Marchesini second model , 1993 .

[23]  K. Furuta.  Sliding mode control of a discrete system , 1990 .

[24]  Wu-Sheng Lu,et al.  Some new results on stability robustness of two-dimensional discrete systems , 1994, Multidimens. Syst. Signal Process..

[25]  Xinping Guan,et al.  Robust optimal guaranteed cost control for 2D discrete systems , 2001 .

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

[27]  Yau-Tarng Juang,et al.  Design of variable structure control for fuzzy nonlinear systems , 2008, Expert Syst. Appl..

[28]  Lihua Xie,et al.  H∞ filtering of 2-D discrete systems , 2000, IEEE Trans. Signal Process..

[29]  H. Salarieh,et al.  Control of stochastic chaos using sliding mode method , 2009 .

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

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

[32]  Zidong Wang,et al.  Robust stability of two-dimensional uncertain discrete systems , 2003, IEEE Signal Processing Letters.

[33]  Krzysztof Galkowski,et al.  A 2D Systems Approach to Iterative Learning Control with Experimental Validation , 2008 .

[34]  Tzuu-Hseng S. Li,et al.  Design of interval type-2 fuzzy sliding-mode controller , 2008, Inf. Sci..