Robust H∞ sliding mode control for uncertain discrete singular T‐S fuzzy Markov jump systems

Abstract

This paper mainly explored the problem of stability in terms of discrete singular T‐S fuzzy Markov jump systems with uncertainties and external disturbances. A new sliding mode controller is proposed for this type of system. Firstly, a common sliding surface that can be shared by all subsystems of discrete singular systems is designed, so the jumping effects could be weakened. Secondly, the proof of stochastic admissibility of the closed‐loop dynamic system is provided by deriving the linear matrix inequality (LMI) technique. Thirdly, an appropriate sliding mode control (SMC) law is designed to satisfy the discrete reaching condition. And, finally, a simulation is offered to illustrate the effectiveness of the derived results.

Extended dissipative output‐feedback control for discrete‐time bidirectional associative memory neural networks via delay‐partitioning approach

“…Meanwhile, the study on the behavior of a system in terms of energy it can store or dissipate has a great research interest since it gives a physical and intuitive interpretation of problems such as dissipativity [27, 28], $$$ {H}_{\infty } $$$ [29, 30], $$$ {L}_2 $$$‐ $$$ {L}_{\infty } $$$ [31], and passivity [32] performances. In Zhang et al [33], the concept of extended dissipativity performance has been introduced as the unified framework of all the above robust performances.…”

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

“…Furthermore, when sensor failures are considered, a dissipative filter of FMJSs with incomplete transition probability is proposed in [25]. Moreover, in [26][27][28], other control and filtering methods of FMJSs with complete transition probability have been presented, but these results rarely involve the control problem of incomplete transition probability.…”

Adaptive sliding mode control for semi‐Markov jump uncertain discrete‐time singular systems

“…During the recent two decades, numerous scholars have carried out thorough research on SS, for example, the theory of continuous-time SS has been systematically explored with attention to the robust control problem in Reference 1, and discrete-time (DT) SS with delay and external disturbance is interested in Reference 2, meanwhile, researchers have also devoted their attention to stability study of singular Markov jump systems. 3,4 Markov process is a highly regarded stochastic process and discussions about it can be found in a large number of studies. [3][4][5][6][7] A simple hypothesis of the Markov process is that its future is only relevant to its present.…”

“…3,4 Markov process is a highly regarded stochastic process and discussions about it can be found in a large number of studies. [3][4][5][6][7] A simple hypothesis of the Markov process is that its future is only relevant to its present. But this hypothesis is restrictive on the distribution of sojourn-time (ST) in each mode, that is, the ST obeys geometric and exponential distributions in the discrete and continuous situations, respectively, which is a big drawback of applying the Markov process.…”

“…Singular systems (SSs) can describe practical problems more accurately and are widely used in the intensive research of modern control theory. During the recent two decades, numerous scholars have carried out thorough research on SS, for example, the theory of continuous‐time SS has been systematically explored with attention to the robust control problem in Reference 1, and discrete‐time (DT) SS with delay and external disturbance is interested in Reference 2, meanwhile, researchers have also devoted their attention to stability study of singular Markov jump systems 3,4 …”