Applications of Mathematics, Vol. 68, No. 3, pp. 305-327, 2023
Finite time stability and relative controllability of second order linear differential systems with pure delay
Mengmeng Li, Michal Fečkan, JinRong Wang
Received November 23, 2021. Published online November 30, 2022.
Abstract: We first consider the finite time stability of second order linear differential systems with pure delay via giving a number of properties of delayed matrix functions. We secondly give sufficient and necessary conditions to examine that a linear delay system is relatively controllable. Further, we apply the fixed-point theorem to derive a relatively controllable result for a semilinear system. Finally, some examples are presented to illustrate the validity of the main theorems.
Keywords: finite time stability; relative controllability; second order; delayed matrix function
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Affiliations: Mengmeng Li, Department of Mathematics, Guizhou University, Huaxi, Guiyang, Guizhou 550025, P. R. China, e-mail: mmli@gzu.edu.cn; Michal Fečkan, Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Mlynská dolina, 842 48 Bratislava, Slovakia; Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73 Bratislava, Slovakia, e-mail: Michal.Feckan@fmph.uniba.sk, feckan@mat.savba.sk; JinRong Wang (corresponding author), Department of Mathematics, Guizhou University, Huaxi, Guiyang, Guizhou 550025, P. R. China, e-mail: jrwang@gzu.edu.cn
