Output Feedback Asynchronous Fuzzy SMC of Nonlinear Markov Jump Systems via Hidden Mode Detections

Abstract

This work is concerned with the asynchronous output feedback sliding mode control (SMC) of stochastic nonlinear Markov jump systems (MJSs) via Takagi–Sugeno fuzzy models. Due to some real-world environment limitations, the actual system modes that are not directly available for controller synthesis are known as hidden modes. Then the sliding surface/sliding mode controller modes are featured as observable modes, and the relationship between these two concepts is established by employing emission probabilities. As a two-layer stochastic process, the hidden Markov model (HMM) governs the jump parameters and characterizes the asynchronous mode switching phenomenon between the original plant and the sliding surface/sliding mode controller. By integrating the sliding surface with the dynamical features of fuzzy MJSs, the dynamics of the sliding motion are described by constructing a T–S fuzzy singular MJS. Under a unified convexification setup, novel dissipative performance and stochastic stability analysis results on the sliding motion are proposed. In view of the full MJS states also not measurable, a novel observed-mode-based asynchronous output feedback dynamic SMC synthesis approach is propounded to ensure the MJSs’ states are located in a vicinity of the sliding surface. Illustrative simulation examples are finally provided to validate the superiority and effectiveness of the developed scheme.