×

Uniform asymptotic stability in infinite delay systems. (English) Zbl 0804.34068

Using the technique of Lyapunov functionals, the author derives conditions for uniform asymptotic stability of infinite delay functional differential systems of the type \(x'(t)= f(t,x_ t)\), where \(x(t)\in \mathbb{R}^ n\) and \(x_ t(s)= x(t+ s)\), \(s\leq 0\). Integro-differential equations with infinite delay are considered as illustration of the stability results obtained.

MSC:

34K20 Stability theory of functional-differential equations
34D20 Stability of solutions to ordinary differential equations
45J05 Integro-ordinary differential equations
PDFBibTeX XMLCite
Full Text: DOI