Robust H∞ SMC of uncertain switched systems with time delay

This paper investigates the robust H_infin sliding mode control problem for a class of uncertain switched delay systems. A single sliding surface is constructed such that the reduced-order equivalent sliding motion restricted to the sliding surface is completely invariant to all admissible uncertainties. For cases of known delay and unknown delay, the existence conditions of the sliding surface are proposed respectively. The corresponding hysteresis switching laws are designed to stabilize the sliding motion with H_infin disturbance attenuation level gamma. Furthermore, variable structure controllers are developed to drive the state of the switched system to reach the single sliding surface in finite time and remains on it thereafter. Finally, a numerical example is given to illustrate the effectiveness of the proposed design method.