Stability of Hybrid Systems with Proportional Delay Based on Pachpatte's Integral Inequalities
A class of hybrid impulsive and switching systems with proportional delay was studied in this paper.For proportional delay,converting proportional delay into constant delay by time transformation is adopt-ed in the literature to obtain the stability results combined with the corresponding criteria.Without time trans-formation,switched Lyapunov function and Pachpatte's integral inequalities were employed in this paper to es-tablish new general criteria for exponential stability and asymptotic stability under arbitrary conditional impul-sive switching.Finally,an example was given to illustrate the theoretical results.It was shown that the chaotic system with proportional delay tends to be stable by the designed impulsive control.
stabilityimpulsive and switching systemsproportional delayPachpatte's integral inequalities
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