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ℋ∞ mode reduction for two-dimensional discrete state-delayed systems.

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Název: ℋ∞ mode reduction for two-dimensional discrete state-delayed systems.
Autoři: Wu, L., Shi, P., Gao, H., Wang, C.
Zdroj: IEE Proceedings -- Vision, Image & Signal Processing; Dec2006, Vol. 153 Issue 6, p769-784, 16p, 2 Charts, 1 Graph
Témata: MATHEMATICAL models, MATHEMATICAL inequalities, DISCRETE-time systems, DIGITAL control systems, AUTOMATIC control systems, PRINCIPAL components analysis
Abstrakt: The problem of ℋ∞ model reduction for two-dimensional (2-D) discrete systems with delay in state is considered. The mathematical model of 2-D systems is established on the basis of the well-known Fornasini–Marchesini local state-space. First, conditions are established to guarantee the asymptotic stability and a prescribed noise attenuation level in the ℋ∞ sense for the underlying system. For a given stable system, attention is focused on the construction of a reduced-order model, which approximates the original system well in an ℋ∞ norm sense. Sufficient conditions are proposed for the existence of admissible reduced-order solutions. Since these obtained conditions are not expressed as strict linear matrix inequalities (LMIs), the cone complementary linearisation method is exploited to cast them into sequential minimisation problems subject to LMI constraints, which can be readily solved using standard numerical software. These obtained results are further extended to more general cases whose system states contain multiple delays. Two numerical examples are provided to demonstrate the effectiveness of the proposed techniques. [ABSTRACT FROM AUTHOR]
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Databáze: Biomedical Index
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Abstrakt:The problem of ℋ∞ model reduction for two-dimensional (2-D) discrete systems with delay in state is considered. The mathematical model of 2-D systems is established on the basis of the well-known Fornasini–Marchesini local state-space. First, conditions are established to guarantee the asymptotic stability and a prescribed noise attenuation level in the ℋ∞ sense for the underlying system. For a given stable system, attention is focused on the construction of a reduced-order model, which approximates the original system well in an ℋ∞ norm sense. Sufficient conditions are proposed for the existence of admissible reduced-order solutions. Since these obtained conditions are not expressed as strict linear matrix inequalities (LMIs), the cone complementary linearisation method is exploited to cast them into sequential minimisation problems subject to LMI constraints, which can be readily solved using standard numerical software. These obtained results are further extended to more general cases whose system states contain multiple delays. Two numerical examples are provided to demonstrate the effectiveness of the proposed techniques. [ABSTRACT FROM AUTHOR]
ISSN:1350245X
DOI:10.1049/ip-vis:20050372