2023/08/10 by Vladyslav Bivziuk, Bivziuk, Vladyslav, Sergey Dashkovskiy +3
Mathematics · #Differential Equations and Boundary Problems #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Differential Equations Analysis #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2308.05615
openalex publication_date 2023/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a linear impulsive system in an infinite-dimensional Banach space. It is assumed that the moments of impulsive action satisfy the averaged dwell-time condition and the linear operator on the right side of the differential equation generates an analytic semigroup in the state space. Using commutator identities, we prove a comparison theorem that reduces the problem of asymptotic stability of the original system to the study of a simpler system with constant dwell-times. An illustrative example of a linear impulsive system of parabolic type in which the continuous and discrete dynamics are both unstable is given.