Sliding mode control with integral sliding surface for linear uncertain impulsive systems with time delays

Abstract

This paper devotes to the problem of sliding mode control (SMC) for linear uncertain impulsive systems with time delays and matched disturbances. An SMC scheme based on a novel integral-type sliding function with an impulse regulation term is proposed. The sliding function is designed so that the finite-time reachability of the sliding surface can be guaranteed for any given impulses. A linear delayed state feedback control law with switching gains is introduced to stabilize the resulting sliding mode dynamics, which is able to improve robust performance against parameter uncertainty. The existence conditions of the delayed state feedback control laws are derived by employing a piecewise discontinuous Lyapunov functional. It is shown that the desired switching gains can be obtained by solving a set of LMIs through a convex optimization procedure. Finally, the correctness and validity of the theoretical results are fully verified in a practical application with several different types of impulse inputs.