Spectral factorization and LQ-optimal regulation for multivariable distributed systems
作者:
FRANKM. CALLIER,
JOSEPH WINKIN,
期刊:
International Journal of Control
(Taylor Available online 1990)
卷期:
Volume 52,
issue 1
页码: 55-75
ISSN:0020-7179
年代: 1990
DOI:10.1080/00207179008953524
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
A necessary and sufficient condition is proved for the existence of a bistable spectral factor (with entries in the distributed proper-stable transfer function algebra 𝒜-) in the context of distributed multivariable convolution systems with no delays; a by-product is the existence of a normalized coprime fraction of the transfer function of such a possibly unstable system (with entries in the algebra ℬ of fractions over 𝒜-). We next study semigroup state-space systems SGB with bounded sensing and control (having a transfer function with entries in ℬ) and consider its standard LQ-optimal regulation problem having an optimal state feedback operator K0. For a system SGB, a formula is given relating any spectral factor of a (transfer function) coprime fraction power spectral density to K0; a by-product is the description of any normalized coprime fraction of the transfer function in terms of K0. Finally, we describe an alternative way of finding the solution operator K0of the LQ-problem using spectral factorization and a diophantine equation: this is similar to Theorem 2 of Kucera (1981) for lumped systems
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