Passivity-based robust sliding mode synthesis for uncertain delayed stochastic systems via state observer

In this paper, the problem of passivity-based sliding mode control (SMC) for uncertain delayed stochastic systems (DSS) within state-observer framework is under consideration. A novel linear sliding surface is first presented with the aid of the provided observer and output information, and a new sufficient condition on the passivity and mean square exponential stability of the underlying closed-loop system during the sliding mode is then derived by employing the stochastic stability theory and linear matrix inequality approach. Further, an associated SMC law is designed to guarantee the arrival of the sliding surface almost surely via the adaptive methodology. Finally, two illustrative examples concerning the desirable performance of the system are conducted to confirm the effectiveness and superiority of the proposed method.