Passivity-Based Asynchronous Control for Markov Jump Systems

Abstract

Abstract-This paper studies the problem of passivity-based asynchronous control for discrete-time Markov jump systems.The asynchronization phenomenon appears between the system modes and controller modes, which is described by a hidden Markov model. Accordingly, the resultant closed-loop system is named as a hidden Markov jump system. By utilizing the matrix inequality technique, three equivalent sufficient conditions are proposed to ensure the stochastic passivity of the hidden Markov jump systems. Based on the established conditions, the design of asynchronous controller, which covers synchronous controller and mode-independent controller as special cases, is addressed. A numerical example is given to demonstrate the effectiveness of the derived results.

Asynchronous control of T‐S fuzzy chaotic systems via a unified model using the hidden Markov model subject to strict dissipativity

“…Remark Under actual conditions, the information of the system accessible by the controller is usually inaccurate . In other words, the real mode of the system is hidden from the controller, which will produce the situation that the controller is the system‐mode observation value.…”

“…So far, the asynchronous control has been involved in many research fields. The asynchronous controller was designed to ensure the passive performance of the system by the new hidden Markov model (HMM) . The asynchronous controller for the network control system was achieved .…”

Observer‐based finite‐time stabilization for discrete‐time switched singular systems with quadratically inner‐bounded nonlinearities

“…Stability and L 2 ‐gain analysis for switched systems and switched delay systems were discussed in the works of Zhang and Shi and Sun et al The nonfragile reduced‐order dynamic output feedback H ∞ control for switched systems with ADT switching was discussed in the work of Zhou et al Adaptive output feedback controller design for switched nonlinear stochastic systems with ADT was considered in the work of Niu et al The problems L 2 ‐gain analysis for switched delay systems and switched linear systems with ADT were investigated in the works of Lin et al Finite‐time stabilization and H ∞ finite‐time control for switched nonlinear systems were discussed in the works of Wang et al, Xiang and Xiao, and Zong et al, respectively. Event‐triggered finite‐time resilient control, asynchronous finite‐time filter, and event‐triggered finite‐time control for networked switched systems were discussed in the works of Ren et al Asynchronous control and asynchronous filtering for Markov switched systems were discussed in the works of Wu et al…”

Observer‐based H∞ control for Markovian jump systems with time‐varying delays and incomplete transition rates

“…Recently, the problems of the stability analysis and controller design for MJSs have became the hot issues, such as robust H ∞ control with saturating actuator, stability analysis with singular MJSs, and H ∞ filters design . On the hypothesis of completely known transition rates, some new results on H ∞ control, sliding mode control, stability, stabilization, and passivity have been reported in other works . On the other hand, in many engineering systems, it is difficult to measure or estimate all transition rates.…”