Asynchronous Stochastic Controller Design for a Class of Markov Jump Linear Systems

This paper investigates asynchronous controller design problem for a class of continuous-time Markov jump linear systems. The mentioed asynchronous phenomenon is a case in which the system and the controller Markov chainsare not matched, however they are relevant according to certain probabilities. This phenomenon describes a realistic and practical situation which arises as a result of inaccurate observation of the system’s Markov chain. The proposed design scheme considers the closed-loop system as a unified Markov jump linear system and utulizes the multiple Lyapunov function approach. By this approach, firstly, the stabilizability of the closed-loop system is ensured and then the asynchronous state-feedback controller is synthesizesed. The designed controller is formulated in terms of linear matrix inequalities; which are easy to check. A numerical example illustrates the usefulness of the developed method.