Periodically multiple state-jumps impulsive control systems with impulse time windows

In this paper, we list a kind of periodically control system with each of its period contains multiple impulses, whose occurrences are limited to small time intervals, i.e., impulse time windows, but are unknown. We first propose three new mathematical models of this system, namely periodically single state-jumps impulsive control systems with impulse time windows, periodically double state-jumps impulsive control systems with impulse time windows and periodically triple state-jumps impulsive control systems with impulse time windows, then by induction, we obtain periodically multiple state-jumps impulsive control systems with impulse time windows. Next, we study the stability of them and obtain their stability criteria by LMIs. Finally Chua׳s oscillator is controlled by using three different kinds of methods obtained in this paper.