Sliding Mode Control of Vibration in Uncertain Time-delay Systems

This paper presents a proportional-integral sliding mode control (PISMC) methodology for the robust control of vibration in a linear uncertain system with state and input delays. The systems are assumed to have structured, unmatched and time-varying parameter uncertainties. 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 achieve a prescribed H-infinity norm bound of disturbance attenuation for all admissible uncertainties without the state predictor. Furthermore, this scheme assures robustness against state delays, input delays, parameter uncertainties and disturbances simultaneously. Simulation results demonstrate the efficacy of the proposed control methodology.