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Partial stability of nonlinear systems of ordinary differential equations with a small parameterстатья
Информация о цитировании статьи получена из
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Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 27 мая 2015 г.
- Авторы: Anashkin O.V., Khapaev M.M.
- Журнал: Differential Equations
- Том: 31
- Номер: 3
- Год издания: 1995
- Издательство: Pleiades Publishing, Inc.
- Местоположение издательства: New York, USA
- Первая страница: 341
- Последняя страница: 351
- Аннотация: The paper is devoted to the partial stability problem for the system $\dot x = X(t,x, \mu)$, $x \in\bbfR^n$ with respect to the variables $x_1, \dots, x_m$ $(m < n)$ under a small parameter $\mu \ge 0$. The authors introduce the notions of partial $\mu$-stability and asymptotic partial $\mu$-stability for this system. The $\mu$-stability means that for sufficiently small $\mu$ all system trajectories which are close to the origin at the moment $t = t_0$ remain so for all $t > t_0$. The unperturbed system $\dot x = X(t,x,0)$ is assumed to be nonasymptotically stable. The main result consists in obtaining new sufficient conditions for partial $\mu$-stability of the original system. Those are given in terms of positive definiteness of a Lyapunov-type auxiliary function $v(t,x)$ with respect to $x_1, \dots, x_m$. A couple of example are considered for third-order dynamic systems.
- Добавил в систему: Хапаев Михаил Михайлович