Fuzzy-model-based robust control of Markov jump nonlinear systems with incomplete transition probabilities and uncertain packet dropouts

Interval type-2 fuzzy Markov jump systems (IT2FMJSs) have received much attention because they can well describe complex nonlinear systems with uncertainties and stochastic system mode switching. However, the transition probabilities of fuzzy MJSs (FMJSs) 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 partially unknown, and packet dropouts of data transmission are uncertain in this study. Compared with the previous studies, the main advantages of this work are as follows: (1) To analyze stochastic stability and reduce conservatism of existing approaches, a novel Lyapunov function that depends on both system mode and fuzzy basis function is constructed; (2) the existence of a mode-dependent and fuzzy-basis-dependent state feedback controller is revealed; (3) stochastic stability of closed-loop system with a desired H-8 performance is established, and the problem of incomplete transition probabilities and uncertain packet dropouts has been completely addressed. An illustrative example of a robot arm is used to demonstrate the effectiveness and practicality of the proposed control strategy. By virtue of the proposed strategy, the effects of incomplete transition probabilities and uncertain packet dropouts on IT2FMJSs have been completely alleviated.

Automated summary

This study proposes a novel method for interval type-2 fuzzy Markov jump systems (IT2FMJSs) to describe complex nonlinear systems with uncertainties and stochastic system mode switching. Unlike previous studies, this method considers partially unknown transition probabilities between system modes switching and uncertain packet dropouts of data transmission. By constructing a new Lyapunov function that depends on both system mode and fuzzy basis function, stochastic stability is analyzed and conservatism of existing approaches is reduced. The existence of a mode-dependent and fuzzy-basis-dependent state feedback controller is revealed, and the stochastic stability of the closed-loop system with a desired H-8 performance is established, addressing the problem of incomplete transition probabilities and uncertain packet dropouts. An illustrative example of a robot arm validates the effectiveness and practicality of the proposed control strategy, which completely alleviates the effects of incomplete transition probabilities and uncertain packet dropouts on IT2FMJSs.