Title :
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
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;
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
Print_ISBN :
978-1-4244-3871-6
Electronic_ISBN :
0191-2216
DOI :
10.1109/CDC.2009.5399626
