  In this paper, we propose new algebraic Gramians for continuous-time linear
switched systems, which satisfy generalized Lyapunov equations. The main
contribution of this work is twofold. First, we show that the ranges of those
Gramians encode the reachability and observability spaces of a linear switched
system. As a consequence, a simple Gramian-based criterion for reachability and
observability is established. Second, a balancing-based model order reduction
technique is proposed and, under some sufficient conditions, stability
preservation and an error bound are shown. Finally, the efficiency of the
proposed method is illustrated by means of numerical examples.
