Output Feedback Control for Nonlinear 2-D Discrete Systems with Time-Varying State Delays

Abstract

In this paper, we study stability analysis and stabilization problems for a class of nonlinear two-dimensional (2-D) discrete systems with time-varying state delays, described by local state-space (LSS) Fornasini-Marchesini (FM) second model. The upper and lower bounds of time-varying state delays are positive integers and the nonlinearity satisfies Lipschitz condition. First, a stability criteria is proposed through introducing a new Lyapunov function. Then a dynamic output feedback controller is designed to assure the stability of nonlinear 2-D time-varying systems. Moreover, the output feedback system matrices can be obtained by solving linear matrix inequalities (LMIs). Finally, a numerical example is given to demonstrate the effectiveness of our results.

Stability analysis for 2‐D switched Takagi‐Sugeno fuzzy systems with stable and unstable subsystems

“…Meantime, it is well known that the phenomenon of time‐delay is one of the inevitable problems in the operation of industrial equipment. And the delay‐dependent method is more reasonable and less conservative than the delay‐independent case [30], especially with a diminutive time‐delay. Up to now, few of papers have studied the problem of 2‐D switched systems with time delays through designing MDADT [16] switching methods, and it is greatly significative and challengeable to study the stability of 2‐D time‐delay switching fuzzy systems with stable and unstable subsystems by designing a switching signal.…”