| Автор | Teel, Andrew R. |
| Автор | Praly, Laurent |
| Дата выпуска | 2000 |
| dc.description | We consider differential inclusions where a positive semidefinite function of the solutions satisfies a class-${\mathcal{KL}}$ estimate in terms of time and a second positive semidefinite function of the initial condition. We show that a smooth converse Lyapunov function, i.e., one whose derivative along solutions can be used to establish the class-${\mathcal{KL}}$ estimate, exists if and only if the class-${\mathcal{KL}}$ estimate is robust, i.e., it holds for a larger, perturbed differential inclusion. It remains an open question whether all class-${\mathcal{KL}}$ estimates are robust. One sufficient condition for robustness is that the original differential inclusion is locally Lipschitz. Another sufficient condition is that the two positive semidefinite functions agree and a backward completability condition holds. These special cases unify and generalize many results on converse Lyapunov theorems for differential equations and differential inclusions that have appeared in the literature. |
| Формат | application.pdf |
| Издатель | EDP Sciences |
| Копирайт | © EDP Sciences, SMAI, 2000 |
| Тема | Differential inclusions |
| Тема | Lyapunov functions |
| Тема | uniform asymptotic stability. |
| Название | A smooth Lyapunov function from a class-${\mathcal{KL}}$ estimate involving two positive semidefinite functions |
| Тип | research-article |
| DOI | 10.1051/cocv:2000113 |
| Electronic ISSN | 1262-3377 |
| Print ISSN | 1292-8119 |
| Журнал | ESAIM: Control, Optimisation and Calculus of Variations |
| Том | 5 |
| Первая страница | 313 |
| Последняя страница | 367 |
| Аффилиация | Teel Andrew R.; ECE Department, University of California, Santa Barbara, CA 93106, U.S.A.; teel@ece.ucsb.edu. |
| Аффилиация | Praly Laurent; Centre Automatique et Systèmes, École des Mines de Paris, 35 rue Saint Honoré, 77305 Fontainebleau Cedex, France; praly@cas.ensmp.fr. |
