Control of a group of systems whose communication channels are assigned by a semi-Markov process

This technical note is concerned with the problem of medium access constraint for a group of networked systems. The scheduling of each subsystem is defined by a stochastic protocol, which can be modelled by a semi-Makov chain with a time-varying transition probability matrix. The resulting closed-loop nonlinear systems are a semi-Markovian jump system with delay. Sufficient conditions for exponential mean-square stability of the resulting closed-loop systems are derived via a Lyapunov–Krasovskii method. Based on the stability criterion, the controller gain of each subsystem is designed. A simulation example is used to demonstrate the effectiveness of proposed method.