Summary: A Necessary and Sufficient Condition for Robust Asymptotic Stabilizability of
Continuous-Time Uncertain Switched Linear Systems
Hai Lin and Panos J. Antsaklis
Abstract-- The main contribution of this paper is a nec-
essary and sufficient condition derived for the existence of
asymptotically stabilizing switching laws for a class of switched
linear systems with time-variant parametric uncertainties.
This result improves upon the sufficient only conditions found
in the literature. The method is based on polyhedral Lyapunov-
like functions, which represent generalizations of polytopic
Lyapunov functions in the classical sense.
The stability issues of switched systems have been of
increasing interest in the recent decade, see for example
,  and the references cited therein. One of the most
elusive problems in the switched systems literature has been
the switching stabilizability problem, that is under what
condition it is possible to stabilize a switched system by
properly designing switching control laws.
In the switching stabilization literature, most of the work