Construction Method of Approximate Stochastic Lyapunov Functions using Quantization of Markov Process

• Nishimura Yuki

  Graduate School of Science and Engineering, Yamaguchi University

• Yamashita Yuh

  Graduate School of Information Science and Technology, Hokkaido University

Bibliographic Information

Other Title

• Ｍａｒｋｏｖ過程の量子化を用いた確率的Ｌｙａｐｕｎｏｖ関数の近似構築
• Markov カテイ ノ リョウシカ オ モチイタ カクリツテキ Lyapunov カンスウ ノ キンジ コウチク

Abstract

The existence of stochastic Lyapunov functions assures that the systems are stable in probability. However, general scheme of obtaining stochastic Lyapunov functions has not been introduced yet. This paper extends the authors’ previous method[21] obtaining Lyapunov functions for deterministic cases to stochastic cases. In the method, difference-approximation scheme[6,10] and quantization of Markov processes[1,14] are used to approximate Lyapunov equations by linear quantum-like equations. We propose a method of obtaining approximate stochastic Lyapunov functions for nonlinear stochastic systems by superimposing the eigenfunctions of the quantum-like equations. <br>

Journal

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

  Transactions of the Institute of Systems, Control and Information Engineers 22 (8), 295-302, 2009

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

Keywords

• nonlinear stochastic system
• stochastic Lyapunov function
• finite-difference approximation
• quantization
• Markov process
• Schrödinger equation
• eigenvalue problem

Details

• CRID: 1390001205165384064
• NII Article ID: 10026193857
• NII Book ID: AN1013280X
• DOI: 10.5687/iscie.22.295
• ISSN: 2185811X
• ISSN: 13425668
• NDL BIB ID: 10321118
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I10321118
• Text Lang: ja
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed