1. Exponential stability of systems of vector delay differential equations with applications to second order equations
- Author
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Elena Braverman and Leonid Berezansky
- Subjects
34K20, 34K06, 34K25 ,Differential equation ,Applied Mathematics ,Second order equation ,Dynamical Systems (math.DS) ,010103 numerical & computational mathematics ,Delay differential equation ,01 natural sciences ,Measure (mathematics) ,Matrix (mathematics) ,Exponential stability ,Matrix function ,0103 physical sciences ,FOS: Mathematics ,Order (group theory) ,0101 mathematics ,Mathematics - Dynamical Systems ,010301 acoustics ,Analysis ,Mathematical physics ,Mathematics - Abstract
Various results and techniques, such as Bohl-Perron theorem, a priori solution estimates, M-matrices and the matrix measure, are applied to obtain new explicit exponential stability conditions for the system of vector functional differential equations $$ \dot{x_i}(t)=A_i(t)x_i(h_i(t)) +\sum_{j=1}^n \sum_{k=1}^{m_{ij}} B_{ij}^k(t)x_j(h_{ij}^k(t)) + \sum_{j=1}^n\int\limits_{g_{ij}(t)}^t K_{ij}(t,s)x_j(s)ds,~i=1,\dots,n. $$ Here $x_i$ are unknown vector functions, $A_i, B_{ij}^k, K_{ij}$ are matrix functions, $h_i,h_{ij}^k, g_{ij}$ are delayed arguments. Using these results, we deduce explicit exponential stability tests for second order vector delay differential equations., 14 pages
- Published
- 2021