Relative controllability of delay differential systems with impulses and linear parts defined by permutable matrices

This paper investigates the relative controllability of delay differential systems with linear impulses and linear parts defined by permutable matrices. We use the impulsive delay Grammian matrix to discuss the relatively controllability of impulsive linear delay controlled systems and we use the Krasnoselskii's fixed point theorem to discuss the relatively controllability of impulsive semilinear delay controlled systems. Finally, two examples are presented to illustrate our theoretical results.

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