Stability analysis and stabilisation for a class of 2-D nonlinear discrete systems

Abstract

This article is concerned with stability analysis and stabilisation problems for a class of two-dimensional (2-D) nonlinear discrete systems. First, the stability condition is derived for 2-D systems with nonlinearity by exploiting the Lyapunov method. Based on this result, a state feedback controller and an output feedback controller are designed to achieve stability for the closed-loop system. Next, H _∞ controllers are given in terms of the linear matrix inequality (LMI). Finally, some numerical examples are used to illustrate the effectiveness of the results.

Keywords:

• stability
• 2-D discrete systems
• nonlinear systems
• linear matrix inequality (LMI)
• bounded realness
• H _∞ control

Acknowledgement

This work is jointly supported by the National Natural Science Foundation of China under Grant No. 60874078, No. 60674014, National Science Foundation for Distinguished Young Scholars of P.R. China under Grant No. 60625303, and Specialised Research Fund for the Doctoral Programme of Higher Education under Grant No. 20070288055, 200802880024.