Shorten, Robert N. and Narendra, Kumpati S. and Mason, Oliver
(2003)
A Result on Common Quadratic Lyapunov Functions.
IEEE Transactions on Automatic Control, 48 (1).
pp. 110-113.
ISSN 0018-9286
Abstract
In this note, we define strong and weak common quadratic
Lyapunov functions (CQLFs) for sets of linear time-invariant (LTI) sys-
tems. 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.
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