| Texto completo | |
| Autor(es): |
Costa, E. F.
;
Val, João Bosco Ribeiro do
[2]
Número total de Autores: 2
|
| Tipo de documento: | Artigo Científico |
| Fonte: | IEEE Transactions on Automatic Control; v. 50, n. 5, p. 691-695, 2005. |
| Área do conhecimento: | Engenharias - Engenharia Elétrica |
| Assunto(s): | Matemática Teoria de sistemas e controle Equações de Riccati |
| Resumo | |
This note addresses the jump linear quadratic problem of Markov jump linear systems and the associated algebraic Riccati equation. Necessary and sufficient conditions for stability of the optimal control and positiveness of Riccati solutions are developed. We show that the concept of weak detectability is not only a sufficient condition for the finiteness of cost functional to imply stability of the associated trajectory, but also a necessary one. This, together with a characterization developed here for the kernel of the Riccati solution, allows us to show that the control solution stabilizes the system if and only if the system is weakly detectable, and that the Riccati solution is positive-definite if and only if the system is weakly observable. The connection between the algebraic Riccati equation and the control problem is made, as far as the minimal positive-semidefinite solution for the algebraic Riccati equation is identified with the optimal solution of the linear quadratic problem. Illustrative numerical examples and comparisons are included. (AU) | |
| Processo FAPESP: | 03/06736-7 - Controle e filtragem de sistemas estocásticos markovianos com saltos nos parâmetros |
| Beneficiário: | João Bosco Ribeiro do Val |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |