Robust H∞ Control of Uncertain Switched Systems: a Sliding Mode Control Design

This paper develops a new method to the robust H∞ control problem for a class of uncertain switched systems by constructing a single robust H∞ sliding surface. The method consists of two phases. One is to construct a single sliding surface such that the reduced-order equivalent sliding motion restricted to the sliding surface is robustly stabilizable with H∞ disturbance attenuation level γ under a hysteresis switching law; the other phase is to design variable structure controllers of subsystems to drive the state of the switched system to reach the single sliding surface in finite time and remain on it thereafter. A numerical example is given to illustrate the effectiveness of the proposed method.