Projected generalized discrete-time periodic Lyapunov equations and balanced realization of periodic descriptor systems

Eric King Wah Chu; Hung Yuan Fan; Wen Wei Lin

doi:10.1137/040606715

Projected generalized discrete-time periodic Lyapunov equations and balanced realization of periodic descriptor systems

Eric King Wah Chu, Hung Yuan Fan, Wen Wei Lin

Research output: Contribution to journal › Article › peer-review

43 Citations (Scopus)

Abstract

From the necessary and sufficient conditions for complete reachability and observability of periodic descriptor systems with time-varying dimensions, the symmetric positive semidefinite reachability/observability Gramians are defined. These Gramians can be shown to satisfy some projected generalized discrete-time periodic Lyapunov equations. We propose a numerical method for solving these projected Lyapunov equations, and give an illustrative numerical example. As an application of our results, the balanced realization of periodic descriptor systems is discussed.

Original language	English
Pages (from-to)	982-1006
Number of pages	25
Journal	SIAM Journal on Matrix Analysis and Applications
Volume	29
Issue number	3
DOIs	https://doi.org/10.1137/040606715
Publication status	Published - 2007
Externally published	Yes

Keywords

Balanced realization
Descriptor systems
Hankel singular values
Periodic systems
Reachability and observability Gramians

ASJC Scopus subject areas

Analysis

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10.1137/040606715

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AB - From the necessary and sufficient conditions for complete reachability and observability of periodic descriptor systems with time-varying dimensions, the symmetric positive semidefinite reachability/observability Gramians are defined. These Gramians can be shown to satisfy some projected generalized discrete-time periodic Lyapunov equations. We propose a numerical method for solving these projected Lyapunov equations, and give an illustrative numerical example. As an application of our results, the balanced realization of periodic descriptor systems is discussed.

KW - Balanced realization

KW - Descriptor systems

KW - Hankel singular values

KW - Periodic systems

KW - Reachability and observability Gramians

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Projected generalized discrete-time periodic Lyapunov equations and balanced realization of periodic descriptor systems

Abstract

Keywords

ASJC Scopus subject areas

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