Stochastic Sliding Mode Control for Parametric Uncertain Systems Using a Functional Observer

Abstract

This chapter addresses the problem of sliding mode control (SMC) design using functional observers (FO) for discrete-time stochastic systems with norm-bounded parametric uncertainty in the system matrix. SMC is a powerful, robust control technique to stabilise discrete-time systems. However, the application of SMC becomes difficult when the system states are inaccessible for feedback. Hence the proposed method uses an FO-based approach for estimating SMC design. To mitigate the side effect of the parametric uncertainty on the estimation error, a sufficient condition for stability is provided based on Gershgorin’s circle theorem. The feasibility and effectiveness of our derived results are illustrated through a simulation example.