Relative controllability of impulsive multi-delay differential systems
Zhongli You
Guizhou University
Michal Fečkan
Comenius University in Bratislava
JinRong Wang
Guizhou University
Donal O’Regan
National University of Ireland
Published 2022-01-01


impulsive multi-delay differential systems
impulsive multi-delay Gramian matrix
relative controllability

How to Cite

You Z., Fečkan M., Wang J. and O’Regan D. (2022) “Relative controllability of impulsive multi-delay differential systems”, Nonlinear Analysis: Modelling and Control, 27(1), pp. 70-90. doi: 10.15388/namc.2022.27.24623.


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.

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