Stability and guaranteed cost control for linear impulsive systems with random impulses: Application to stochastic event-triggered control

This paper proposes a systematic framework for stability and guaranteed cost control of linear impulsive systems subject to random time- and event-triggering impulses. Moment stability criteria and design methods of time- and event-triggered controllers with guaranteed quadratic performance for the impulsive system are established. It shows that the proposed event-triggered controller in the sense that it guarantees at least the same quadratic performance function bound as the designed time-triggered guaranteed cost controller, however, with a larger, or at most equal, average inter-transmission time. Based on the proposed framework of random-impulses systems, a stochastic dynamic event-triggered control strategy is proposed to solve sampled-data control systems in the presents of sporadic measurements or stochastic sampling. Numerical simulations illustrate the effectiveness of the proposed theoretical results.