Relative controllability of impulsive multi-delay differential systems - You, Zhongli; Fečkan, Michal; Wang, JinRong; O’Regan, Donal (Nonlinear Analysis: Modelling and Control, 2022)
In this paper, relative controllability of impulsive multi-delay differential systems in finite dimensional space are studied. By introducing the impulsive multi-delay Gramian matrix, a necessary and sufficient condition, and the Gramian criteria, for the relative controllability of linear systems is given. Using Krasnoselskii’s fixed point theorem, a sufficient condition for controllability of semilinear systems is obtained. Numerically examples are given to illustrate our theoretically results.
Keywords: impulsive multi-delay differential systems; impulsive multi-delay Gramian matrix; relative controllability