Asynchronous Event-Triggered Control for Polynomial Fuzzy-Model-Based Markov Jump Systems With Complex Transition Probabilities

This article investigates the asynchronous event-triggered control problem for nonlinear Markov jump systems with complex transition probabilities. The nonlinear dynamics are captured by a polynomial fuzzy model, with fewer fuzzy rules and stronger approximation capacity compared with Takagi–Sugeno fuzzy counterpart. In view of engineering applications, system mode information is not fully identified, including the mode state and the mode transitions. Here, a hidden Markov model is utilized to serve as a detector of the original system mode. The transition probability of the system and the associated conditional transition probability for the joint process are both assumed to be general, which contains unknown or inaccurately known values. An event-based mode-dependent fuzzy controller is then constructed such that the considered nonlinear Markov jump systems can be stabilized, for the purpose of reducing data transmission and power consumption. With the aid of a new decoupling strategy, feasible conditions are derived and included in sum-of-square-based theorems. Further the concept of imperfectly premise matching scheme is introduced to facilitate the membership-function-dependent stability analysis, so as to inject richer information of the membership function and obtain less conservative results. The flexibility of controller design is, thus, endowed. Examples are given to show the effectiveness of our obtained results.