Stabilization of semi‐Markovian jump systems by a stochastically scheduled controller

Abstract

This article considers the stabilization problem of continuous‐time semi‐Markovian jump systems. A kind of stochastically scheduled controller is proposed to realize the aim. It could also suffer a case that no controller is added to subsystems during some time slices. Based on a Lyapunov approach, sufficient conditions for such a controller are presented with LMI forms. Both sojourn times of jump signal and distribution properties of stochastic scheduling are involved and have positive roles in getting better performances. Two special cases about mode‐dependent and mode‐independent controllers are directly obtained. A practical example is given to verify the effectiveness and superiority of the proposed methods.

Stabilizing control of Markovian jump systems with sampled switching and state signals and applications

“…On the other hand, in order to balance the above two methods, some other control methods such as partially mode-dependent controller, 25 partial information controller, 26 disordered or unmatched controller, 24 scheduling controller 27,28 and quantity limited controller 29 were proposed. Though some general situations about stabilizing control of MJSs were studied, there are still some problems to be considered.…”

Hybrid asynchronous sliding mode control for hidden Markovian jump systems under optimized design

“…Two essentials of MJSs are subsystem model, that is, the configuration of each mode, and transition probabilities between subsystems. It is noted that the transition probabilities are often known a priori for controller design, and the control signal interacts with the activated subsystem so as to stabilize systems or achieve the desired performance, for example, in References 4‐6 for certain or complete transition probability matrix cases, in References 7 and 8 for uncertain or incomplete cases.…”

Sampled‐data synchronization of singular Markovian jump system: Application to DC motor model

“…Markovian jump systems (MJSs) emerge as a promising research topic since they have the ability to describe an extensive range of physical models when there are sudden changes or random perturbations in the environment. With intensified and extensive research by scholars, MJSs can be applied to a widespread range of practical engineering problems, such as bilateral teleoperation systems [1], resource allocation in a server cluster [2], four distributed generators [3], and vertical take-off landing (VTOL) helicopter model [4]. Simultaneously, singular systems are a class of systems that have a wider degree of applicability than regular systems, comprising slow-variable subsystems characterised with differential or difference expressions and fast-variable subsystems characterised by algebraic expressions.…”