The controllability of non-autonomous evolution systems is an important and difficult topic in control theory. In this paper, we study the approximate controllability of semilinear non-autonomous evolution systems with state-dependent delay. The theory of linear evolution operators is used instead of C₀-semigroup to discuss the problem. Some sufficient conditions of approximate controllability are formulated and proved here by using the resolvent operator condition. Finally, two examples are provided to illustrate the applications of the obtained results.
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Xianlong Fu (2017) studied this question.