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

2017 ◽  
Vol 38 ◽  
pp. 39-46 ◽  
Author(s):  
JinRong Wang ◽  
Zijian Luo ◽  
Michal Fečkan
Keyword(s):  
Differential Systems ◽  
Relative Controllability ◽  
Delay Differential Systems ◽  
Delay Differential

scholarly journals Relative controllability of impulsive multi-delay differential systems

2022 ◽  
Vol 27 (1) ◽  
pp. 70-90
Author(s):  
Zhongli You ◽  
Michal Fečkan ◽  
JinRong Wang ◽  
Donal O’Regan
Keyword(s):  
Dimensional Space ◽  
Sufficient Condition ◽  
Finite Dimensional Space ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Differential Systems ◽  
Relative Controllability ◽  
Finite Dimensional ◽  
Delay Differential Systems ◽  
Delay Differential ◽  
Necessary And Sufficient

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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