Stability of Ulam-Hyers and existence of solutions for impulsive time-delay semi-linear systems with non-permutable matrices
Mathematics, vol.8, no.9, 2020 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 8 Issue: 9
- Publication Date: 2020
- Doi Number: 10.3390/math8091493
- Journal Name: Mathematics
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
- Keywords: Delayed matrix exponential, Impulsive delay equation, Stability
- Open Archive Collection: Article
- Azerbaijan State University of Economics (UNEC) Affiliated: No
Abstract
In this paper, the stability of Ulam-Hyers and existence of solutions for semi-linear time-delay systems with linear impulsive conditions are studied. The linear parts of the impulsive systems are defined by non-permutable matrices. To obtain solution for linear impulsive delay systems with non-permutable matrices in explicit form, a new concept of impulsive delayed matrix exponential is introduced. Using the representation formula and norm estimation of the impulsive delayed matrix exponential, sufficient conditions for stability of Ulam-Hyers and existence of solutions are obtained.