H ∞ Control of 2-D Discrete State Delay Systems

This paper is concerned with the H∞ control problem of 2-D discrete state delay systems described by the Roesser model. The condition for the system to have a specified H ∞ performance is derived via the linear matrix inequality (LMI) approach. Furthermore, a design procedure for H ∞ state feedback controllers is given by solving a certain LMI. The design problem of optimal H ∞ controllers is formulated as a convex optimization problem, which can be solved by existing convex optimization techniques. Simulation results are presented to illustrate the effectiveness of the proposed results.

[1]  S. Niculescu.  Delay Effects on Stability: A Robust Control Approach , 2001 .

[2]  P. Khargonekar,et al.  State-space solutions to standard H/sub 2/ and H/sub infinity / control problems , 1989 .

[3]  J. Doyle,et al.  Robust and optimal control , 1995, Proceedings of 35th IEEE Conference on Decision and Control.

[4]  Lihua Xie,et al.  LMI approach to output feedback stabilization of 2-D discrete systems , 1999 .

[5]  R. Bracewell.  Two-dimensional imaging , 1994 .

[6]  E. Fridman,et al.  Delay-dependent stability and H ∞ control: Constant and time-varying delays , 2003 .

[7]  Magdi S. Mahmoud,et al.  New results on delay-dependent control of time-delay systems , 2005, IEEE Transactions on Automatic Control.

[8]  P. Khargonekar,et al.  State-space solutions to standard H2 and H∞ control problems , 1988, 1988 American Control Conference.

[9]  Keon Young Yi,et al.  Control of a Balance-Beam with Unknown Loads Using the Restoration Angle of a Gimbal , 2006 .

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

[11]  J. Kurek,et al.  The general state-space model for a two-dimensional linear digital system , 1985 .

[12]  Lihua Xie,et al.  H[∞] control and filtering of two-dimensional systems , 2002 .

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

[14]  Li Yu,et al.  An LMI approach to guaranteed cost control of linear uncertain time-delay systems , 1999, Autom..

[15]  G. Marchesini,et al.  Algebraic Realization Theory of Two-Dimensional Filters , 1975 .

[16]  P. Gahinet,et al.  A linear matrix inequality approach to H∞ control , 1994 .

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

[18]  Donald D. Givone,et al.  Multidimensional Linear Iterative Circuits - General Properties , 1972, IEEE Trans. Computers.

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