Fuzzy-Model-Based Robust Control of Markov Jump Nonlinear Systems With Incomplete Transition Probabilities and Uncertain Packet Dropouts

Abstract Interval type-2 fuzzy Markov jump systems (IT2FMJSs) have received much attention because they can better describe complex nonlinear systems with uncertainties and stochastic system mode switching. Over the past decade, many excellent results of fuzzy MJSs (FMJSs) have been reported. However, the transition probabilities which govern the dynamic behaviour of MJSs have been assumed to be completely known, limiting real-world applications of existing results. Different from the previous studies, transition probabilities between system modes switching are partly unknown, and packet dropouts of data transmission are uncertain in this study. The main contributions of this work are: (1) To analyze stochastic stability and reduce conservatism, a novel Lyapunov function which both depends on system mode and fuzzy basis function is constructed; (2) The existence of a mode-dependent and fuzzy-basis-dependent state-feedback controller is investigated; (3) The closedloop system is stochastically stable with a desired H∞ performance, thereby addressing the problem of incomplete transition probabilities and uncertain packet dropouts. An illustrative example of a robot arm is used to demonstrate the effectiveness and practicality of the proposed approach. By virtue of the proposed approach, the effects of incomplete transition probabilities and uncertain packet dropouts on IT2FMJSs are alleviated.