Stochastic Sliding Mode Control for Parametric Uncertain Systems Using Functional Observer

Abstract

This brief addresses the problem of sliding mode control (SMC) design using functional observer (FO) for discrete-time stochastic systems with norm-bounded parametric uncertainty in the system matrix. SMC is a most powerful, robust control technique to stabilize discrete-time systems. However, the application of SMC becomes difficult when the system states are not accessible for feedback. Hence the proposed method uses FO-based approach for estimating SMC design. To mitigate the side effect of the parameter uncertainty on the estimation error, a sufficient condition of stability is provided based on Gershgorin disc theorem. The feasibility and effectiveness of our derived results are illustrated through a simulation example.