State space formulas for a suboptimal rational Leech problem II: Parametrization of all solutions
| Autor: | Frazho, A.E., ter Horst, S., Kaashoek, M.A. |
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| Přispěvatelé: | Mathematics |
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
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| Zdroj: | Frazho, A E, ter Horst, S & Kaashoek, M A 2015, ' State space formulas for a suboptimal rational Leech problem II: Parametrization of all solutions ', Operator Theory: Advances and Applications, vol. 244, pp. 149-179 . https://doi.org/10.1007/978-3-319-10335-8_8 Operator Theory: Advances and Applications, 244, 149-179 |
| DOI: | 10.1007/978-3-319-10335-8_8 |
| Popis: | For the strictly positive case (the suboptimal case), given stable rational matrix functions $G$ and $K$, the set of all $H^\infty$ solutions $X$ to the Leech problem associated with $G$ and $K$, that is, $G(z)X(z)=K(z)$ and $\sup_{|z|\leq 1}\|X(z)\|\leq 1$, is presented as the range of a linear fractional representation of which the coefficients are presented in state space form. The matrices involved in the realizations are computed from state space realizations of the data functions $G$ and $K$. On the one hand the results are based on the commutant lifting theorem and on the other hand on stabilizing solutions of algebraic Riccati equations related to spectral factorizations. 28 pages |
| Databáze: | OpenAIRE |
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