Robust H∞ Control for Nonlinear Uncertain Switched Descriptor Systems with Time Delay and Nonlinear Input: A Sliding Mode Approach

Abstract

This paper addresses the problem of sliding mode control (SMC) design for a class of uncertain switched descriptor systems with state delay and nonlinear input. An integral sliding function is designed and an adaptive sliding mode controller for the reaching motion is then synthesised such that the trajectories of the resulting closed-loop system can be driven onto a prescribed sliding surface and maintained there for all subsequent times. Moreover, based on a new Lyapunov-Krasovskii functional, a delay-dependent sufficient condition is established such that the admissibility as well as the H∞ performance requirement of the sliding mode dynamics can be guaranteed in the presence of time delay, external disturbances, and nonlinear input which comprises dead-zones and/or sector nonlinearities. The major contributions of this paper of this approach include (i) the closed-loop system exhibiting strong robustness against nonlinear dynamics and (ii) the control scheme enjoying the chattering-free characteristic. Finally, two representative examples are given to illustrate the theoretical developments.