International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 3, Pages 435-440
doi:10.1155/S0161171296000622

Cone valued Lyapunov functions and Lipschitz stability of nonlinear systems of differential equations

Abstract

We introduce a new comparison result which will be an important tool when we apply cone valued Lyapunov like functions. We also introduce new concepts of ϕ0-uniform Lipschitz stability and (λ,λ,ϕ0)-practical stability and employ our comparison result to carry out stability analysis of nonlinear systems. Our results are also applicable to nonlinear perturbed systems.