Dissipativity-Based Asynchronous Repetitive Control for Networked Markovian Jump Systems: 2-D System Approach

Abstract

This article addresses the dissipativity-based asynchronous repetitive control problem for networked Markovian jump systems subject to time delays and partly accessible mode detection probabilities. A hidden Markov model is introduced to describe the asynchronous phenomenon between the system modes and controller modes. Based on this, an asynchronous repetitive controller is proposed. By utilizing the lifting technique, the 1-D delayed Markovian jump system and controller governing equations are converted into a stochastic and closed-loop 2-D delayed model to describe the control and learning actions. Utilizing a stochastic Lyapunov functional, sufficient conditions in terms of matrix inequalities are derived such that the closed-loop system is mean-square stable and achieves the specified $(\mathscr {W}_1,\mathscr {W}_2,\mathscr {W}_3)$ - $\gamma$ -dissipative performance. Under the assumption that the input matrix is full column rank in all modes of operation, a set of feasible sufficient conditions described by linear matrix inequalities is established by making use of the Schur complement. A procedure for synthesizing the controller parameters is also provided. A detailed numerical example with simulation results is presented to validate the proposed dissipativity-based asynchronous repetitive control design scheme.