Controllability and Hyers–Ulam Stability of Differential Systems with Pure Delay

Ahmed M. Elshenhab and Xingtao Wang
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Ahmed M. Elshenhab: School of Mathematics, Harbin Institute of Technology, Harbin 150001, China
Xingtao Wang: School of Mathematics, Harbin Institute of Technology, Harbin 150001, China

Mathematics, 2022, vol. 10, issue 8, 1-18

Abstract: Dynamic systems of linear and nonlinear differential equations with pure delay are considered in this study. As an application, the representation of solutions of these systems with the help of their delayed Mittag–Leffler matrix functions is used to obtain the controllability and Hyers–Ulam stability results. By introducing a delay Gramian matrix, we establish some sufficient and necessary conditions for the controllability of linear delay differential systems. In addition, by applying Krasnoselskii’s fixed point theorem, we establish some sufficient conditions of controllability and Hyers–Ulam stability of nonlinear delay differential systems. Our results improve, extend, and complement some existing ones. Finally, two examples are given to illustrate the main results.

Keywords: controllability; delay differential system; delayed matrix function; Hyers–Ulam stability; delay Gramian matrix; Krasnoselskii’s fixed point theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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