Title :
On positive real lemma for stabilizable and detectable systems
Author :
Kunimatsu, Sadaaki ; Fujii, Teruya ; Ishitobi, Mitsuaki
Author_Institution :
Kumamoto Univ., Kumamoto, Japan
Abstract :
In this paper, we state the positive real lemma for stabilizable and detectable systems. First, without assumptions of controllability and observability, we show the positive real lemma for stable systems under only some constraint with respect to invariant zeros. Moreover we show that the solution of the Lyapunov equation in the positive real lemma is positive definite. Next we show the positive real and strictly positive real lemmas for stabilizable and detectable systems under only that constraint.
Keywords :
Lyapunov methods; controllability; observability; stability; state-space methods; Lyapunov equation; controllability; detectable system; observability; positive real lemma; stabilizable system; Control system synthesis; Control systems; Controllability; Eigenvalues and eigenfunctions; Equations; Linear matrix inequalities; Observability; State-space methods; Transfer functions;
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.2009.5400274
