Title :
A result on common quadratic Lyapunov functions
Author :
Shorten, Robert ; Narendra, Kumpati S. ; Mason, Oliver
Author_Institution :
Hamilton Inst., NUI Maynooth, Ireland
fDate :
1/1/2003 12:00:00 AM
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;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2002.806661
