Necessary and sufficient conditions for finite-time boundedness of linear discrete-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

3226

Lastpage

3231

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 discrete-time systems. The conditions are extensions of those for FTS and are related to a quadratic optimization problem. Sufficient conditions are also derived in terms of difference linear matrix inequalities. Numerical examples show an exact bound and upper bounds of FTB by solving the obtianed conditions.

Keywords

discrete time systems; linear matrix inequalities; linear systems; quadratic programming; stability; time-varying systems; difference linear matrix inequalities; finite-time boundedness; finite-time stability; linear time-varying discrete-time system; quadratic optimization; Eigenvalues and eigenfunctions; Linear matrix inequalities; Lyapunov method; Missiles; Space vehicles; Stability; Sufficient conditions; Time varying systems; Upper bound; 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.2009.5399626

Filename

5399626