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Relative controllability of delay differential systems with impulses and linear parts defined by permutable matrices
Author(s) -
You Zhongli,
Wang JinRong,
O'Regan Donal,
Zhou Yong
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5400
Subject(s) - controllability , permutable prime , mathematics , gramian matrix , controllability gramian , matrix (chemical analysis) , differential (mechanical device) , control theory (sociology) , linear system , point (geometry) , mathematical analysis , pure mathematics , control (management) , eigenvalues and eigenvectors , computer science , artificial intelligence , engineering , aerospace engineering , physics , materials science , geometry , quantum mechanics , composite material
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.