A generalization of piecewise linear Lyapunov functions

Author

Ohta, Yuzo ; Tsuji, Masaaki

Author_Institution

Kobe Univ., Japan

Volume

5

fYear

2003

fDate

9-12 Dec. 2003

Firstpage

5091

Abstract

The purpose of this paper is to propose a generalization of piecewise linear Lyapunov functions (PLLFs). In original PLLF candidates, functions are parameterized by hyperplanes, which intersect the stability region and stability conditions are formulated as linear programming problems (LPs) in terms of the parameters inserted by the hyperplanes. The piecewise linear hyperplanes (PLHPs) were introduced to reduce the size of LPs and produce a new class of PLLF candidates; however, applicable systems of this idea were restricted in a certain class of systems. In this paper, this restriction is removed and new PLLF candidates are characterized as the sum of piecewise linear functionals corresponding to PLHPs.

Keywords

Lyapunov methods; linear programming; piecewise linear techniques; stability; linear programming problems; piecewise linear Lyapunov functions; piecewise linear functionals; piecewise linear hyperplanes; stability conditions; stability region; Linear matrix inequalities; Linear programming; Lyapunov method; Nonlinear systems; Piecewise linear techniques; Research and development; Stability analysis;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2003. Proceedings. 42nd IEEE Conference on

ISSN

0191-2216

Print_ISBN

0-7803-7924-1

Type

conf

DOI

10.1109/CDC.2003.1272443

Filename

1272443