Robust control of uncertain time-delay systems via sliding mode control and LMI-H∞ technique

This paper presents a proportional-integral sliding mode control (PISMC) methodology for a class of linear uncertain systems with state delays. The systems are assumed to have structured, mismatched, and time-varying parameter uncertainties as well as mismatched and bounded external disturbances. Based on Lyapunov stability theorem and linear matrix inequality (LMI) H-infinity technique, a sufficient condition is derived to guarantee the global stability of the dynamics and a prescribed H-infinity norm bound of disturbance attenuation for all admissible uncertainties. Furthermore, this scheme assures robustness against state delays, parameter uncertainties and disturbances. Finally, an example is given to illustrate the feasibility of the proposed control methodology.