Sliding mode control of switched uncertain linear systems: Designing robust H∞ sliding surface

The robust H_∞ control problem for a class of uncertain switched linear systems by using the variable structure control is investigated. A robust H_∞ single sliding surface is shown to exist as long as a convex combination of the subsystems of the switched system is robustly stabilizable with disturbance attenuation level γ. A switching law is constructed via the single Lyapunov function technique. Variable structure controllers of subsystems are designed so as the resulting closed-loop system guarantees the robust H_∞ performance. An illustrative example and simulation results are given to demonstrate the effectiveness of the proposed design method.