Analysis of Nonlinear Systems in Specified Regions of the State Space by Using Density Functions Characterizing Positively Invariant Sets

• MASUBUCHI Izumi

  Graduate School of Engineering, Hiroshima University

Bibliographic Information

Other Title

• 正不変集合を特徴づける密度関数を用いた状態空間の所定領域における非線形システムの解析
• セイ フヘン シュウゴウ オ トクチョウヅケル ミツド カンスウ オ モチイタ ジョウタイ クウカン ノ ショテイ リョウイキ ニ オケル ヒセンケイ システム ノ カイセキ

Abstract

This paper is concerned with analysis of positive invariance and regional almost convergence of nonlinear systems by using density functions. It is shown that if there exists a density function that is positive inside a set and zero on its boundary then the set is positively invariant and almost all of the trajectories starting from the set are convergent. This result is applicable to controller synthesis for nonlinear systems by using convex optimization with satisfying state and input constraints. Furthermore, converse theorems are provided to ensure the existence of such density functions under mild assumptions.

Journal

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

  Transactions of the Institute of Systems, Control and Information Engineers 19 (12), 453-461, 2006

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

Keywords

• nonlinear systems
• positively invariant sets
• convergence of trajectries
• convex formulation of synthesis
• density functions

Details

• CRID: 1390282680141810816
• NII Article ID: 10018420210
• NII Book ID: AN1013280X
• DOI: 10.5687/iscie.19.453
• ISSN: 2185811X
• ISSN: 13425668
• NDL BIB ID: 8573032
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I8573032
• Text Lang: ja
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed