Adaptive Control of Nonlinear Semi-Markovian Jump T–S Fuzzy Systems With Immeasurable Premise Variables via Sliding Mode Observer

The issue of observer-based adaptive sliding mode control of nonlinear Takagi–Sugeno fuzzy systems with semi-Markov switching and immeasurable premise variables is investigated. More general nonlinear systems are described in the model since the selections of premise variables are the states of the system. First, a novel integral sliding surface function is proposed on the observer space, then the sliding mode dynamics and error dynamics are obtained in accordance with estimated premise variables. Second, sufficient conditions for stochastic stability with an <inline-formula> <tex-math notation="LaTeX">${H}_{\infty }$ </tex-math></inline-formula> performance disturbance attenuation level <inline-formula> <tex-math notation="LaTeX">${\gamma }$ </tex-math></inline-formula> of the sliding mode dynamics with different input matrices are obtained based on generally uncertain transition rates. Third, an observer-based adaptive controller is synthesized to ensure the finite time reachability of a predefined sliding surface. Finally, the single-link robot arm model is provided to verify the control scheme numerically.