A Lyapunov Stability Analysis of 2-D Discrete-Time Systems Based on the Behavioral Approach

• KOJIMA Chiaki

  Graduate School of Informatics, Kyoto University

• TAKABA Kiyotsugu

  Graduate School of Informatics, Kyoto University

Bibliographic Information

Other Title

• ビヘイビアアプローチに基づく２‐Ｄ離散時間システムのＬｙａｐｕｎｏｖ安定解析
• ビヘイビアアプローチ ニ モトヅク 2 D リサン ジカン システム ノ Lyapunov アンテイ カイセキ

Abstract

This paper is concerned with a Lyapunov stability analysis of a two-dimensional (2-D) discrete-time system described by a high-order partial difference equation in the behavioral setting. We first formulate the autonomy and asymptotic stability of 2-D discrete-time behavior in terms of the characteristic set over Z². A sufficient condition for asymptotic stability is derived in terms of quadratic difference forms. This condition can be numerically checked by solving a certain four-variable polynomial matrix equation. It also turns out that the present result generalizes some existing stability conditions for the Fornasini-Marchesini state-space model to the behavioral setting.

Journal

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

  Transactions of the Institute of Systems, Control and Information Engineers 20 (2), 60-68, 2007

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

Keywords

• Lyapunov stability theory
• behavioral approach
• quadratic difference form
• polynomial matrix
• two-dimensional system

Details

• CRID: 1390001205165643136
• NII Article ID: 10022000089
• NII Book ID: AN1013280X
• DOI: 10.5687/iscie.20.60
• ISSN: 2185811X
• ISSN: 13425668
• NDL BIB ID: 8634291
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I8634291
• Text Lang: ja
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
• Abstract License Flag: Disallowed