Necessary and sufficient conditions for finite-time boundedness of linear continuous-time systems

Author

Ichihara, Hiroyuki ; Katayama, Hitoshi

Author_Institution

Dept. of Syst. Design & Inf., Kyushu Inst. of Technol., Iizuka, Japan

fYear

2009

fDate

15-18 Dec. 2009

Firstpage

3214

Lastpage

3219

Abstract

Finite-time stability (FTS) requires that the state of a system does not exceed a certain bound during a specified time interval for given bound on the initial state. The concept of FTS introduced exogenous inputs is called finite time boundedness (FTB). This paper gives necessary and sufficient conditions for FTB of linear time-varying continuous-time systems. The conditions are extensions of existing necessary and sufficient for FTS. The sufficient conditions for FTB are also given in terms of differential linear matrix inequalities, which can be relaxed by matrix sum of squares, univariate polynomials. Numerical examples show the solvability of the sufficient conditions.

Keywords

computability; continuous time systems; linear matrix inequalities; linear systems; polynomials; stability; time-varying systems; differential linear matrix inequalities; finite-time boundedness; finite-time stability; linear continuous-time systems; matrix sum of squares; time-varying continuous-time systems; univariate polynomials; Eigenvalues and eigenfunctions; Linear matrix inequalities; Lyapunov method; Missiles; Polynomials; Space vehicles; Stability; Sufficient conditions; Time varying systems; Vehicle dynamics;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on

Conference_Location

Shanghai

ISSN

0191-2216

Print_ISBN

978-1-4244-3871-6

Electronic_ISBN

0191-2216

Type

conf

DOI

10.1109/CDC.2009.5400748

Filename

5400748