Positive real control for uncertain 2-D discrete systems in general model

This paper discusses the problem of positive real control for uncertain two-dimensional discrete systems in general model (2-D GM) with norm-bounded parameter uncertainties. Attention is focused on the design of dynamic output feedback controllers, which guarantee that the closed-loop system is robustly stable and the closed-loop transfer function is extended strictly positive real (ESPR) for all admissible uncertainties. A sufficient condition for ESPR of 2-D GM is first presented. Based on this, the explicit parameters of the desired output feedback controller are designed using a linear matrix inequality (LMI). Finally, a numerical example to demonstrate the effectiveness and feasibility of the proposed method is provided.

[1]  K. Galkowski,et al.  Positive real control for uncertain two-dimensional systems , 2002 .

[2]  Lihua Xie,et al.  Positive real control problem for uncertain linear time-invariant systems , 1995 .

[3]  C. A. Desoer,et al.  Nonlinear Systems Analysis , 1978 .

[4]  Graham C. Goodwin,et al.  Adaptive filtering prediction and control , 1984 .

[5]  Shengyuan Xu,et al.  Positive real control for 2-D discrete delayed systems via output feedback controllers , 2008 .

[6]  D. Bernstein,et al.  Explicit construction of quadratic lyapunov functions for the small gain, positivity, circle, and popov theorems and their application to robust stability. part II: Discrete-time theory , 1993 .

[7]  R. Kálmán.  LYAPUNOV FUNCTIONS FOR THE PROBLEM OF LUR'E IN AUTOMATIC CONTROL. , 1963, Proceedings of the National Academy of Sciences of the United States of America.

[8]  Lei Guo,et al.  Robust H∞ Control for Uncertain Two-Dimensional Discrete Systems Described by the General Model via Output Feedback Controllers , 2008 .

[9]  P. Khargonekar,et al.  Robust stabilization of uncertain linear systems: quadratic stabilizability and H/sup infinity / control theory , 1990 .

[10]  D. S. Bernstein,et al.  Explicit construction of quadratic Lyapunov functions for the small gain, positivity, circle and Popov theorems and their application to robust stability , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[11]  Zhang Qing-ling.  Design of positive real state feedback control for continuous-time descriptor systems based on LMI , 2004 .

[12]  Weiqun Wang,et al.  The detectability and observer design of 2-D singular systems , 2002 .

[13]  P. Khargonekar,et al.  Solution to the positive real control problem for linear time-invariant systems , 1994, IEEE Trans. Autom. Control..

[14]  Lihua Xie,et al.  Positive real analysis and synthesis of uncertain discrete time systems , 2000 .