Lyapunov Equations, Inequalities and Stability Theorems for Periodic Systems

• KANO Hiroyuki

  School of Science and Engineering, Tokyo Denki University

• NISHIMURA Toshimitsu

  School of Engineering, Tokyo Engineering University

Bibliographic Information

Other Title

• 周期システムに対するリアプノフ方程式, 不等式および安定性定理
• シュウキ システム ニ タイスル リアプノフ ホウテイシキ フトウシキ オヨビ アンテイセイ テイリ

Abstract

Lyapunov equations and inequalities are studied in connection with the stability of linear periodic systems. First, as preliminaries, existing results on Lyapunov equations in time-invariant systems are summarized in the form of equivalence theorems. Then, based on those results, existence conditions are derived for positive-definite or nonnegative-definite periodic solutions of periodic Lyapunov differential equations and inequalities with reference to the detectability and observability. Such conditions are stated all as equivalent conditions for the system to be either asymptotically stable or stable. Brief discussions are included also for periodic Lyapunov difference equations in discrete-time periodic systems.

Journal

• Transactions of the Institute of Systems, Control and Information Engineers

  Transactions of the Institute of Systems, Control and Information Engineers 13 (3), 134-140, 2000

  THE INSTITUTE OF SYSTEMS, CONTROL AND INFORMATION ENGINEERS (ISCIE)

Keywords

• Lyapunov equation
• stability
• periodic system
• observability
• detectability

Details

• CRID: 1390001205165333888
• NII Article ID: 10004472919
• NII Book ID: AN1013280X
• DOI: 10.5687/iscie.13.3_134
• ISSN: 2185811X
• ISSN: 13425668
• NDL BIB ID: 5292898
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I5292898
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
• Abstract License Flag: Disallowed