Lipschitz and Asymptotic Stability for Perturbed Nonlinear Differential Systems

Abstract

The present paper is concerned with the notions of Lipschitz and asymptotic stability for perturbed nonlinear differential system knowing the corresponding stability of nonlinear differential system. We investigate Lipschitz and asymtotic stability for perturbed nonlinear differential systems. The main tool used is integral inequalities of the Bihari-type, in special some consequences of an extension of Bihari's result to Pinto and Pachpatte, and all that sort of things.

Uniformly Lipschitz Stability and Asymptotic Property in Perturbed Nonlinear Differential Systems

“…Choi et al [6,7] examined Lipschitz and exponential asymptotic stability for nonlinear functional systems. Goo [11] and Choi et al [3,5] investigated Lipschitz and asymptotic stability for perturbed differential systems. Also, Im and Goo [13] investigated asymptotic property for solutions of the perturbed functional differential systems.…”

Lipschitz and Asymptotic Stability of Perturbed Functional Differential Systems

“…Choi et al [6,7] examined Lipschitz and exponential asymptotic stability for nonlinear functional systems. Also, Goo et al [11,13] investigated Lipschitz and asymptotic stability for perturbed differential systems.…”

Asymptotic Property for Perturbed Nonlinear Functional Differential Systems

“…Choi et al [6,7] examined Lipschitz and exponential asymptotic stability for nonlinear functional systems. Also, Goo [11] and Choi and Goo [2,4] investigated Lipschitz and asymptotic stability for perturbed differential systems.…”