Dynamic event-triggered control for Markovian jump linear systems with time-varying delay

In this article, the problem of dynamic event-triggered control (ETC) for Markovian jump linear systems (MJLSs) with time-varying delay is investigated. First, the original system is transformed into an interconnection system with input-output form. Then, the dynamic ETC is proposed to reduce the transmission frequency. Meanwhile, the conditions of stochastic stability are proposed by constructing a novel stochastic Lyapunov-Krasovskii functional and using the scaled stochastic small-gain theorem. Further, the controller design method is presented to stabilize the closed-loop MJLSs with time-varying delay. The merit of this article lies in that the conservatism for stability results is reduced and the transmission efficiency is improved by reducing the event-triggered times, which is made possible by designing dynamic ETC. Finally, two numerical examples are provided to demonstrate the advantages and effectiveness of the proposed methods.