Exponential stability of systems of vector delay differential equations with applications to second order equations

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 $$\dot{x_i}(t)=A_i(t)x_i(h_i(t))+\sum _{j=1}^n\sum _{k=1}^{m_{ij}}{B}_{ij}^k(t)x_j(h_{ij}^k(t))+\sum _{j=1}^n\underset{g_{ij}(t)}{\overset{t}{\int }}{K}_{ij}(t,s)x_j(s)ds,i=1,\dots ,n.$$ 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

References in corpus (1)

• On stability of linear neutral differential equations with variable delays