Asynchronous output feedback control for Markov jump systems under dynamic event‐triggered strategy

Abstract

This article addresses the synthesis of static output feedback stabilization via employing event‐based control, for discrete‐time Markov jump systems subject to limited bandwidth and mismatched modes. The event‐triggered communication strategy with an extra dynamic variable is considered in the design of controller to alleviate transmission burden. Then, for the purpose of further improving system performance, a special triggering threshold constructed as a diagonal matrix is introduced. Asynchronous behavior caused by mismatched modes between the controller and controlled systems is depicted by utilizing a hidden Markov model. With the assistance of output feedback theory, an asynchronous event‐based output feedback control law is sufficiently formulated to achieve the stochastic stabilization with desired H∞$$ {H}_{\infty } $$ performance. Ultimately, an illustrative example is implemented to verify the feasibility of theoretical results.

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.…”

“…(3) The involved transition rates of the two Markov chains can be unknown or just their boundaries be known, showing more generality than the existing works. It is worth saying that when the detective probabilities turn to be partly bounded ones, the existing methods proposed in [1,[25][26][27][28][29][30][31] are not applicable anymore, but the proposed method can still work.…”