On the stability of invariant sets of systems with impulse effect |
| |
Authors: | Alexander O Ignatyev |
| |
Institution: | Institute for Applied Mathematics and Mechanics of National Academy of Sciences of Ukraine, R. Luxemburg Street, 74, Donetsk-83114, Ukraine |
| |
Abstract: | A system of differential equations with impulse effect is considered. It is assumed that this system has an invariant set M. By means of the direct Lyapunov method, the necessary and sufficient conditions of its uniform asymptotic stability are obtained. The conditions on the perturbations of right hand sides of differential equations and impulse effects, under which the uniform asymptotic stability of the invariant set M of the “nonperturbed” system implies the uniform asymptotic stability of the invariant set of the “perturbed” system, are obtained. The stability properties of invariant sets of periodic systems are also studied. |
| |
Keywords: | Differential equations with impulse effect Stability Lyapunov&rsquo s direct method |
本文献已被 ScienceDirect 等数据库收录! |
|