Self-triggered multi-mode control of Markovian jump systems

This paper is concerned with the problem of self-triggered multi-mode control for a class of Markovian jump systems, in which the system states are transmitted to the controller via a communication network with limited bandwidth. In order to achieve the desired performance of the closed-loop system via utilizing a controller with fewer modes, a mode monitoring mechanism related to the system modes is employed to describe the jumping characteristics among different controller modes. Based on the mode monitoring mechanism, a multi-mode controller is constructed, in which the number of controller modes may be fewer than the one of system modes. Moreover, a self-triggered strategy is developed to reduce network loads, according to which the next triggering instant on state transmission is calculated via the past and current transmitted states at the triggering instants. By introducing a sufficiently small scalar, a solving algorithm is proposed for obtaining the self-triggered multi-mode controller gains to ensure the stochastic stability of the closed-loop system with the given L2 gain performance. Finally, the simulation results are provided to illustrate the proposed self-triggered control scheme.