Controllability and Stability of Non-instantaneous Impulsive Stochastic Multiple Delays System

T. Sathiyaraj () and JinRong Wang ()
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T. Sathiyaraj: UCSI University
JinRong Wang: Guizhou University

Journal of Optimization Theory and Applications, 2024, vol. 201, issue 3, No 2, 995-1025

Abstract: Abstract This paper gives the controllability and Ulam–Hyers–Rassias (U–H–R) stability results for non-instantaneous impulsive stochastic multiple delays system with nonpermutable variable coefficients. The solution for nonlinear non-instantaneous impulsive stochastic systems is presented without the assumption of commutative property on delayed matrix coefficients. The kernel function of the solution operator is defined by sum of noncommutative products of delayed matrix constant coefficients. Sufficient conditions for controllability of linear and nonlinear non-instantaneous impulsive stochastic multiple delays system are established by using the Mönch fixed-point theorem under the proof that the corresponding linear system is controllable. Thereafter, U–H–R stability result is proved. Finally, the theoretical results are verified by a numerical example.

Keywords: Non-instantaneous impulsive differential equations; Controllability; U–H–R stability; Inclusive health; 93B05; 34A37; 93E03 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02430-5

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