Dissipativity-based asynchronous fault detection for T-S fuzzy nonlinear Markov jump systems subject to uncertain probabilities

In this paper, the dissipativity-based asynchronous fault detection problem over unreliable communication is investigated for a class of Takagi-Sugeno fuzzy nonlinear Markov jump systems with time-varying delays and subject to uncertain probabilities. The communication links between the plant and filter are considered to be unreliable, where the stochastic quantization and measurement missing phenomenon are taken into account simultaneously. The asynchronization between the plant and the designed fault detection filter (the random quantizer), is modeled by independent hidden Markov models with a conditional probability matrix, where both the transition probabilities of the plant and the conditional probabilities of the filter are considered to be only partially accessible. By virtue of the Lyapunov stability theory and the slack matrix technique, sufficient conditions guaranteeing the resulting residual system being asymptotically mean square stable and strictly (Q, S, R)-α-dissipative are deduced. And then, the parameters of the desired fault detection filter are explicitly expressed by solving a set of strict linear matrix inequalities. Finally, two examples are utilized to demonstrate the effectiveness and practicability of the proposed design technique.