| Revista: | Journal of the Brazilian Society of Mechanical Sciences and Engineering |
| Base de datos: | PERIÓDICA |
| Número de sistema: | 000312340 |
| ISSN: | 1678-5878 |
| Autores: | Muller, Peter C1 |
| Instituciones: | 1Bergische Universitat Wuppertal, Safety Control Engineering, Wuppertal, Nordrhein-Westfalen. Alemania |
| Año: | 2006 |
| Periodo: | Oct-Dic |
| Volumen: | 28 |
| Número: | 4 |
| Paginación: | 448-452 |
| País: | Brasil |
| Idioma: | Inglés |
| Tipo de documento: | Artículo |
| Enfoque: | Teórico |
| Resumen en inglés | For linear time-invariant (LTI) state space systems it is well-known that its asymptotic stability can be related to solution properties of the Lyapunov matrix equation according to so-called inertia theorems. The question now arises how analogous results can be obtained for LTI descriptor systems (singular systems, differential-algebraic equations). The stability behaviour of a LTI descriptor system is characterized by the eigenvalues of the related matrix pencil. Additionally, by a quadratic Lyapunov function the stability problem can be discussed by solution properties of a generalized Lyapunov matrix equation including a singular coefficient matrix. To overcome this difficult problem of singularity, the Lyapunov matrix equation will be modified such that a regular Lyapunov matrix equation appears and asymptotic stability is preserved. This aim can be reached by shifting the system matrices in a well defined manner. For that the a priori knowledge of an upper bound of the eigenvalues is assumed. It will be discussed how to get such bound. The paper ends with an inertia theorem where the solution properties of a regular modified Lyapunov matrix equation are uniquely related to the asymptotic stability of the LTI descriptor system |
| Disciplinas: | Ingeniería |
| Palabras clave: | Ingeniería mecánica, Sistemas dinámicos, Estabilidad asintótica, Método de Lyapunov, Inercia |
| Keyword: | Engineering, Mechanical engineering, Dynamic systems, Asymptotic stability, Lyapunov method, Inertia |
| Texto completo: | Texto completo (Ver PDF) |
