Griggs, Wynita M. and King, Christopher K. and Shorten, Robert N. and Mason, Oliver and Wulff, Kai
A Geometrical Treatment for Obtaining Necessary and Sufficient
Conditions for Joint Quadratic Lyapunov Function Existence for
State-Dependent, Switched Systems: A Two-Dimensional Case.
Control and Automation, 2009. MED '09. 17th Mediterranean Conference on . ISBN 978-1-4244-4684-1 .
The question of existence of joint quadratic Lyapunov
functions (QLFs) for state-dependent, switched dynamical
systems is given a preliminary geometrical treatment in
this paper. The joint QLF problem for a switched system and
a collection of regions defined by state vectors that determine
when switching occurs consists of finding nonempty intersections
of convex sets of QLFs. The existence of a joint QLF
guarantees switched system stability. Necessary and sufficient
conditions for the existence of a joint QLF are obtained for a
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