Remark 1. Fig. 1 depicts the time response of the state variable of system (1) without impulse switching. It can be seen that the system is stable for the system state variable converges to zeros within 4 second. Fig. 2 depicts the time response of state variable of system (1) with impulse switching. It can be seen that the stable time is shorten to 1.2 second for the existence of the impulsive switching, which shows the effectiveness of our theoretical results.
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