  We study dynamics of a bimodal planar linear switched system with a Hurwitz
stable and an unstable subsystem. For given \textit{flee time} from the
unstable subsystem, the goal is to find corresponding \textit{dwell time} in
the Hurwitz stable subsystem so that the switched system is asymptotically
stable. The dwell-flee relations obtained are in terms of certain smooth
functions of the eigenvalues and (generalized) eigenvectors of the subsystem
matrices. The results are extended to a special class of symmetric bilinear
systems. The results are also extended to a multimodal planar linear switched
system in which the switching is governed by an undirected star graph, where
the internal node corresponds to a Hurwitz stable (unstable, respectively)
subsystem and all the leaves correspond to unstable (Hurwitz stable,
respectively) subsystems. For this multimodal system, dwell-flee relations are
obtained as solutions of a minimax optimization problem.
