Improved results on reachable set synthesis of Markovian jump systems with time-varying delays: General asynchronous control approaches

Abstract

This paper investigates the reachable set synthesis (RSS) issue of Markovian jump systems (MJSs) with time-varying delays via various asynchronous controls. The goal is to devise appropriate asynchronous controllers to assure that the reachable set (RS) of the generated closed-loop dynamic system (CDS) is constrained in the specified region. Firstly, a hidden Markov model (HMM) is used to describe mismatch case among controller modes and system modes. Next, coupling problem of mode mismatch is solved by using an effective inequality condition, and the sufficient conditions for the existence of the asynchronous controllers by linear matrix inequalities (LMIs) are given. Based on the desired asynchronous controllers, the additional reachable set synthesis results of two related controls for the MJSs are obtained. Finally, two simulations are given to demonstrate the feasibility and superiority of the provided methods.