Functional Observer-Based Sliding Mode Control for Parametric Uncertain Discrete-Time Delayed Stochastic Systems

Abstract

This chapter is concerned with the problem of the functional observer-based  sliding mode control (SMC) design for parametric uncertain discrete-time delayed stochastic systems including mismatched parameter uncertainty in the state matrix and in the delayed state matrix. Stability analysis of the sliding function is presented in a time delayed stochastic system with the linear matrix inequality (LMI) approach. Moreover, it is shown that the state trajectories can be driven onto the specified sliding surface despite the presence of state delay, unmatched parameter uncertainty, and stochastic noise in the system. The research is motivated by the fact that system states are not always accessible for the state feedback. Therefore, SMC is estimated using the functional observer technique. To mitigate the side effect of parametric uncertainty on the estimation error, a sufficient condition of stability is proposed based on Gershgorin’s circle theorem. The claims made are validated through numerical simulations.