Title :
A result on common quadratic Lyapunov functions
Author :
Shorten, Robert ; Narendra, Kumpati S. ; Mason, Oliver
Author_Institution :
Hamilton Inst., Maynooth, Ireland
Abstract :
In this paper we define strong and weak common quadratic Lyapunov functions (CQLFs) for sets of linear time-invariant (LTI) systems. We show that the simultaneous existence of a weak CQLF of a special form, and the non-existence of a strong CQLF, for a pair of LTI systems, is characterised by easily verifiable algebraic conditions. These conditions are found to play an important role in proving the existence of strong CQLFs for general LTI systems.
Keywords :
Hermitian matrices; Lyapunov methods; eigenvalues and eigenfunctions; linear systems; stability; Hermitian matrix; LTI systems; eigenvalues; linear time-invariant systems; quadratic Lyapunov functions; stability; switched linear systems; Artificial intelligence; Eigenvalues and eigenfunctions; Equations; Linear systems; Lyapunov method; Sections; Stability; Sufficient conditions; Switching systems;
Conference_Titel :
Decision and Control, 2002, Proceedings of the 41st IEEE Conference on
Print_ISBN :
0-7803-7516-5
DOI :
10.1109/CDC.2002.1184262
