Asynchronous Fuzzy Dynamic Sliding Mode Control for Nonlinear Markov Jump Systems Under Hidden Mode Detections

This article studies the asynchronous dissipative-based sliding mode control (SMC) for nonlinear Markov jump system (MJS) by Takagi–Sugeno (T–S) fuzzy models, which suffer from mismatched parameter uncertainties and exogenous disturbances. The actual system modes are usually not accessible directly for controller design due to some practical environment constraints, and the modes of the sliding surface and controller are characterized as observed modes. The hidden Markov model (HMM) is first utilized to detect the system mode information, which also describes the asynchronous phenomenon of the jump mode between the sliding surface/controller and the original plant. Based on the observed modes, a suitable sliding surface is designed via consisting of both the system states and the control input. By sufficiently exploiting the dynamical features of the fuzzy MJSs and associating with the sliding surface, new sliding surface existence conditions are proposed, which also ensure the stochastic stability (SS) and desired dissipative performance for the sliding motion. Then, a novel asynchronous dynamic SMC law is proposed to drive the fuzzy MJS states into a neighborhood of the designed sliding surface. Finally, simulation studies are conducted to show the validity of the proposed approach.