Abstract
The goal of this paper is to provide systematic approaches to study the feedback control systems governed by impulsive evolution equations in separable reflexive Banach spaces. We firstly give some existence results of mild solutions for the equations by applying the Banach’s fixed point theorem and the Leray–Schauder alternative fixed point theorem with Lipschitz conditions and different types of boundedness conditions. Then, by using the Filippove theorem and the Cesari property, a new set of sufficient assumptions are formulated to guarantee the existence results of feasible pairs for the feedback control systems. Finally, we apply our main result to obtain a controllability result for impulsive evolution equations and two existence results for a class of impulsive differential variational inequalities and impulsive Clarke’s subdifferential inclusions.
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