The fast convergence controller design for a class of Markov jump delay systems with partially known transition rates

Abstract

Fast convergence is one of the core pursuit goals of modern high-performance control systems. This article investigates the fast convergence control problem of Markov jump systems. In order to ensure the feasibility of the fast convergence controller design method, the Lyapunov-Krasovskii functional is constructed based on Lyapunov stability theory in the derivation process of the algorithm. Based on a time-varying proportional function, a distributed control algorithm is designed and the fast convergence controller design method is proposed for the considered systems. The variation of controller gain with time is discussed in sections, and the boundary of controller output is given to make the designed controller more practical for real-world engineering applications. Finally, two simulation examples are given to demonstrate the effectiveness of the proposed method in this paper.