An ISMC approach to robust stabilization of uncertain stochastic time-delay systems

Integral sliding mode control (ISMC) of uncertain stochastic systems with time delay is investigated in this paper. Aiming to remove a very restrictive assumption required in most existing ISMC schemes for stochastic systems, a new ISMC approach is proposed. It is shown that the closed-loop control system trajectories can be kept on the integral sliding surface almost surely since the initial time and the stochastic stability of the sliding motion can be guaranteed in terms of linear matrix inequalities. MATLAB simulation results on a numerical example and a practical stream water quality preserving system are provided to show the effectiveness and advantage of the proposed approaches.