<italic>H</italic>&#x221E; Control Observer-Based for Discrete-Time Singularly Perturbed Systems With Nonlinear Disturbances

Abstract

This paper focuses on the $H\infty $ observer-based control problem for discrete-time singularly perturbed systems (DTSPSs) with nonlinear disturbances. The main contributions of this paper include three aspects: First, a proper observer is constructed. A sufficient condition in terms of linear matrix inequality (LMI) and Lyapunov function is proposed such that the resulting observer error system is asymptotically stable with a prescribed $H_{\infty }$ norm bound for sufficiently small values of the perturbation parameter. Second, based on the input-to-state stability (ISS) property, an observer-based feedback controller is designed such that the resulting closed-loop system is ISS with respect to the observer error. Meanwhile, the $H\infty $ performance index is also satisfied. Then, a workable way for solving the exact upper bound is also given. Finally, two numerical examples are given to demonstrate the validity of the developed method.

Keywords

• Discrete-time singularly perturbed system
• observer
• state feedback
• H∞ control
• linear matrix inequality (LMI)