Exponential stability of an alternate control system with double impulses

Abstract In this paper, we propose a new system called an alternate control system with double impulses. The present system is a cyclic control system, composed of four parts in a circle: to the first and last halves of each period of the system we add different continuous controls, and at the half-period time and the end of each period of the system we add different impulses. We then investigate the exponential stability of the considered system. An example based on Chua’s circuit is provided to confirm the effectiveness of the theoretical result.