Flexible robust sliding mode control for uncertain stochastic systems with time-varying delay and structural uncertainties

This paper presents a new robust sliding mode control (SMC) method for uncertain stochastic systems with time-varying delay, structural uncertainties and the Brownian noise. The proposed method applies singular value decomposition (SVD) to all the structural uncertainties, and introduces adjustable parameters for control design. Then, a less-conservative condition of robust stability and new robust controller for the uncertain stochastic systems are derived via linear matrix inequality (LMI) forms. The reachability of system states to the SMC switching surface is guaranteed by the proposed control rule. It is theoretically proved that the conservatism of the proposed method is less than the previous methods. The simulation demonstrates the correctness of the results.