Guaranteed cost control of uncertain linear systems via discrete-time variable structure control

This paper presents a design of realizing the guaranteed cost control problem for uncertain linear systems via discrete-time variable structure control (VSC) scheme. The uncertainties in the system are assumed to be norm-bounded and time-varying. Based on the discrete-time VSC technique, the proposed controller can drive the system into a pre-specified switching surface to obtain the desired dynamic performance and the chattering phenomenon is eliminated. Sufficient conditions for the existence of guaranteed cost control are presented, and the problem of designing guaranteed cost control is converted to a convex optimization problem with linear matrix inequality (LMI) constraints. Finally, simulation results demonstrate the efficacy of the proposed control methodology.