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 journalArticle

30 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 languageEnglish
Pages (from-to)982-1006
Number of pages25
JournalSIAM Journal on Matrix Analysis and Applications
Volume29
Issue number3
DOIs
Publication statusPublished - 2007 Dec 1

Fingerprint

Balanced Realization
Descriptor Systems
Lyapunov Equation
Periodic Systems
Observability
Reachability
Discrete-time
Positive semidefinite
Time-varying
Numerical Methods
Necessary Conditions
Numerical Examples
Sufficient Conditions

Keywords

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

ASJC Scopus subject areas

  • Analysis

Cite this

Projected generalized discrete-time periodic Lyapunov equations and balanced realization of periodic descriptor systems. / Chu, Eric King Wah; Fan, Hung Yuan; Lin, Wen Wei.

In: SIAM Journal on Matrix Analysis and Applications, Vol. 29, No. 3, 01.12.2007, p. 982-1006.

Research output: Contribution to journalArticle

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