Asynchronous Dissipative Control for Fuzzy Markov Jump Systems

The problem of asynchronous dissipative control is investigated for Takagi–Sugeno fuzzy systems with Markov jump in this paper. Hidden Markov model is introduced to represent the nonsynchronization between the designed controller and the original system. By the fuzzy-basis-dependent and mode-dependent Lyapunov function, a sufficient condition is achieved such that the resulting closed-loop system is stochastically stable with a strictly (<inline-formula> <tex-math notation="LaTeX">$ {\mathcal {Q}}$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$ {\mathcal {S}}$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$ {\mathcal {R}}$ </tex-math></inline-formula>)-<inline-formula> <tex-math notation="LaTeX">$ {\alpha }$ </tex-math></inline-formula>-dissipative performance. The controller parameter is derived by applying MATLAB to solve a set of linear matrix inequalities. Finally, we present two examples to confirm the validity and correctness of our developed approach.