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We study dynamics of a bimodal planar linear switched system with a Hurwitzstable and an unstable subsystem. For given \textit{flee time} from theunstable subsystem, the goal is to find corresponding \textit{dwell time} inthe Hurwitz stable subsystem so that the switched system is asymptoticallystable. The dwell-flee relations obtained are in terms of certain smoothfunctions of the eigenvalues and (generalized) eigenvectors of the subsystemmatrices. The results are extended to a special class of symmetric bilinearsystems. The results are also extended to a multimodal planar linear switchedsystem in which the switching is governed by an undirected star graph, wherethe 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 areobtained as solutions of a minimax optimization problem.

Stability of Bimodal Planar Switched Linear Systems with Both Stable and Unstable Subsystems