Exponential Stabilization of Delayed Discrete-time Linear System via a Hybrid Impulsive Control

This paper investigates exponential stabilization problem of delayed discrete-time linear system (DDLS) via a novel hybrid impulsive control. The hybrid impulsive control consists of time-triggered impulsive control (TTIC) and event-triggered mechanism (ETM). A prescribed exponentially decreasing function serves as the event condition determining when the periodic impulse is free. Compared with the TTIC, the designed hybrid impulsive control strategy can reduce the frequency of controller update and communication burden effectively. It is shown that system state ultimately converges to a level associated with the prescribed parameters. The exponential convergence rate depends on the exponentially decaying rate of prescribed exponentially decreasing function. Finally, one numerical simulation is implemented to verify the validity of the obtained results.