Event-triggered control for Markov jump systems subject to random consecutive packet losses

This paper considers the problem of event-triggered control (ETC) for Markov jump systems (MJSs) with random consecutive packet losses. According to the Bernoulli distribution of a single packet loss, consecutive packet losses are discussed and the corresponding probability distribution is provided. Considering that packet losses cause old triggered data to be used such that Zeno behavior occurs, a hybrid event-triggering scheme (HETS) including a predetermined fixed triggering lower bound is adopted. Then the influences of consecutive packet losses on triggering scheme are presented and new triggering inequalities are derived based on the number of lost packets. By resorting to Lyapunov function method, sufficient conditions including the number of lost packets and its probability distribution are developed to guarantee the stochastic stability of MJSs. Finally, the parameters of HETS and controller gains are designed and the effectiveness of the developed results is illustrated by two numerical examples.