DocumentCode
1123820
Title
A result on common quadratic Lyapunov functions
Author
Shorten, Robert ; Narendra, Kumpati S. ; Mason, Oliver
Author_Institution
Hamilton Inst., NUI Maynooth, Ireland
Volume
48
Issue
1
fYear
2003
fDate
1/1/2003 12:00:00 AM
Firstpage
110
Lastpage
113
Abstract
In this note, 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 nonexistence of a strong CQLF, for a pair of LTI systems, is characterized 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
Lyapunov methods; linear systems; stability; Lyapunov functions; linear time-invariant systems; quadratic Lyapunov functions; simultaneous existence; stability theory; switched linear systems; Eigenvalues and eigenfunctions; Equations; Linear systems; Lyapunov method; Stability; Sufficient conditions; Switching systems;
fLanguage
English
Journal_Title
Automatic Control, IEEE Transactions on
Publisher
ieee
ISSN
0018-9286
Type
jour
DOI
10.1109/TAC.2002.806661
Filename
1166530
Link To Document