Computer generated Lyapunov functions for a class of nonlinear systems

Author

Ohta, Yuzo ; Imanishi, Hiroshi ; Gong, Lei ; Haneda, Hiromasa

Author_Institution

Dept. of Electron. Eng., Kobe Univ., Japan

Volume

40

Issue

5

fYear

1993

fDate

5/1/1993 12:00:00 AM

Firstpage

343

Lastpage

354

Abstract

The problem of constructing Lyapunov functions for a class of nonlinear dynamical systems is considered. The problem is reduced to the construction of a polytope satisfying some conditions. A generalization of the concept of sector condition that it makes possible to evaluate a given nonlinear function by using a set of piecewise-linear functions is proposed. This improvement greatly reduces the conservatism in the stability analysis of nonlinear systems. Two algorithms for constructing such polytopes are proposed, and two examples are shown to demonstrate the usefulness of the results

Keywords

Lyapunov methods; control system analysis computing; nonlinear control systems; piecewise-linear techniques; stability; Lyapunov functions; dynamical systems; nonlinear function; nonlinear systems; piecewise-linear functions; polytope; sector condition; stability analysis; Circuits; Helium; Joining processes; Linear systems; Lyapunov method; Nonlinear dynamical systems; Nonlinear systems; Piecewise linear techniques; Scholarships; Stability analysis;

fLanguage

English

Journal_Title

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.232578

Filename

232578