On reachable set synthesis of delay Markovian jump systems under partially delay‐dependent asynchronous control

Abstract

This paper pays close attention to the reachable set synthesis problem for discrete‐time delayed Markovian jump systems (DDMJSs) under partially asynchronous control. Different from the traditional controller, a class of partially asynchronous controller is proposed, where delay‐free and delay states are comprised and cannot take place at the same time. In addition, Bernoulli variable is used to describe the probability distribution of the above two kinds of states, and the design of feedback controller is considered. On this basis, the sufficient conditions which the state feedback controller is existent are solved effectively by using linear matrix inequalities (LMIs). Furthermore, the results of reachable set synthesis are extended to the DDMJs with uncertain transition probabilities. Finally, several numerical simulations are given to show the effectiveness of the presented methods.

Hidden Markov model‐based asynchronous exponential stabilization for stochastic Markovian jump systems with incomplete controller mode information

“…First, the definition is different. In this paper, we use the transition rates to describe the relationship between the system modes and controller modes (behaving in () and ()), while in [1, 25–31], conditional probability was used, that is, $$$ \mathcal{P}\left\{r(t)=i|\psi (t)=k\right\}={\sigma}_{ik} $$$. Second, we assume the transition rates of both the system and controller to be partly bounded known, while the detection probability $$$ {\sigma}_{ik} $$$ was usually assumed to be exactly known.…”

“…Remark A hidden Markov model is used to govern the controller switching. Unlike the existing results proposed in [1, 25–31], a new relationship between the system modes and controller modes is established, behaving on the transition rates. Note that in [1, 25–31], the detection probabilities had to be exactly known; however, the transition rates can be partly bounded known.…”

“…Unlike the existing results proposed in [1, 25–31], a new relationship between the system modes and controller modes is established, behaving on the transition rates. Note that in [1, 25–31], the detection probabilities had to be exactly known; however, the transition rates can be partly bounded known. This shows more generality than the existing works and can still work when the detection probabilities are uncertain.…”

“…However, most of the traditional methods just addressed the synchronous stability and stabilization problems, which required system modes to be acquired exactly. Although some asynchronous control methods have been proposed for MJSs [1,[25][26][27][28][29][30][31], they mainly fell into two aspects and still posed some limitations. Specifically, most already existing works used the hidden Markov models to facilitate the designed asynchronous controllers, they inevitably assumed the detective probabilities to be fully accessible implicitly.…”

Hidden Markov model‐based approach on real‐time output reachable set synthesis for discrete‐time nonlinear Markovian jump systems

“…It is worth mentioning that the real‐time performance of the NDSs can be satisfied through the proposed control mechanism, which means that the results of the RSE in this article are more real‐time than the previous normal discrete‐time MJSs References 37 and 45 with time‐delay. In addition, compared with References 41 and 46, we eliminate the limitation that the initial condition of the system is zero and extend the state RSS investigation to the output RSS of T‐S fuzzy systems. The article presents an asynchronous control strategy where the controller mode information cannot completely match the system mode information. This kind of mode mismatch phenomenon is consistent with the HMM characteristic.…”