Robust model predictive control for Markovian jump systems under Round-Robin protocol

Abstract

In this paper, a robust model predictive control problem is investigated for a class of Markovian jump systems with polytopic uncertainties. The Round-Robin protocol is utilised to schedule data transmission from the controllers to the actuator in order to reduce the burden of communication and the occupancy of network effects. Moreover, two kinds of transition probability matrices for the Markovian process are considered due to the practical application process, namely the one with polytopic uncertainties and the other with partially unknown entries. Sufficient conditions are established by means of the mixed-mode and token-dependent Lyapunov-like technique such that the closed-loop system is stable in the mean-square sense. In addition, a set of mixed-mode and token-dependent state feedback controllers are designed in terms of minimising a certain upper bound of the worst-case infinite horizon cost function. Finally, some simulation examples are implemented to verify the effectiveness of the proposed design scheme.