Connection of Intermittent Control and Impulsive Control and Extend to Synchronization of Nonlinear Systems

ABSTRACT Since the ideal impulsive signals are difficult to apply in practical control systems, this paper explores the connection from impulsive control to intermittent control via the characteristics and relationships of two control methods, thereby making impulsive control practical. Based on impulsive differential equations and Lyapunov stability theory, a sufficient condition for replacing impulsive control with intermittent control is derived. On this basis, replacement algorithms for the two control methods are presented, including the selection rules of control parameters. Furthermore, the proposed control strategy is extended to achieve the synchronization of nonlinear systems. Moreover, the framework is extended to the case where impulsive intervals are allowed to vary within prescribed time windows. Finally, some simulation examples are presented to verify the validity of the results in this paper.