Robust stability for nonlinear systems with time-varying delay and uncertainties via the h∞ quasi-sliding mode control

Abstract

This paper considers the problem of the robust stability for the nonlinear system with time-varying delay and parameters uncertainties. Based on the H ∞ theorem, Lyapunov-Krasovskii theory, and linear matrix inequality (LMI) optimization technique, the H∞ quasi-sliding mode controller and switching function are developed such that the nonlinear system is asymptotically stable in the quasi-sliding mode and satisfies the disturbance attenuation (H∞-norm performance). The effectiveness and accuracy of the proposed methods are shown in numerical simulations. © 2014 Yi-You Hou and Zhang-Lin Wan.