Reliable Sampled-Data Control of Fuzzy Markovian Systems with Partly Known Transition Probabilities

Abstract

This article presents a fuzzy dynamic reliable sampled-data control design for nonlinear Markovian jump systems, where the nonlinear plant is represented by a Takagi-Sugeno fuzzy model and the transition probability matrix for Markov process is permitted to be partially known. In addition, a generalised as well as more practical consideration of the real-world actuator fault model which consists of both linear and nonlinear fault terms is proposed to the above-addressed system. Then, based on the construction of an appropriate Lyapunov-Krasovskii functional and the employment of convex combination technique together with free-weighting matrices method, some sufficient conditions that promising the robust stochastic stability of system under consideration and the existence of the proposed controller are derived in terms of linear matrix inequalities, which can be easily solved by any of the available standard numerical softwares. Finally, a numerical example is provided to illustrate the validity of the proposed methodology.

Exponential stability of switched Markovian jumping neutral‐type systems with generally incomplete transition rates

“…Therefore, it is necessary to develop the research about Markovian jumping systems with uncertain transition rates. () Sakthivel et al considered an observer‐based dissipative control for Markovian jump systems via delta operators. The authors considered a problem of robust sampled‐data control for uncertain switched neutral systems with probabilistic input delay.…”

Sampled‐data reliable control for T–S fuzzy semi‐Markovian jump system and its application to single‐link robot arm model

“…□ Remark 3 Note that the premise variables may not synchronously arrive at controller because of the network‐induced delays between sampling instants. To overcome the shortage of asynchronous premise variables, the MMF is introduced, which was neglected in [13–15] and obtained results in this paper reduced the conservativeness. Remark 4 In the existing literature, many researchers studied the stability problem of MJSs and proposed good results, for example see [25–27], in which the TRs are time constants. The TRs in the paper are time varying, which illustrate that the proposed conditions in this paper are more general than the existing literature.…”

Finite-time Sliding Mode Control for Interval Type-II Markov Jump Systems with Partially Known Transition Probabilities under Dynamic Event-triggered Scheme

“…However, most of the researcher have only considered the transition probabilities of MJSs are fully known and various results have been investigated in [12] [13]. In practical point of view, the transition probabilities of MJSs are not fully known, due to the presence of channel delays and packet dropout in digital control system, it may be very costly to achieve full known transition probabilities [14] [15]. Hence, it is important and necessary to further investigate more general MJSs together with partially known transition probabilities.…”