Stability of bimodal planar switched linear systems with both stable and unstable subsystems.

We study dynamics of a bimodal planar linear switched system with both stable and unstable subsystems. For given flee time from the unstable subsystem, the goal is to find corresponding dwell time in the stable subsystem so that the switched system is 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 then extended to a multimodal planar linear switched system in which the switching is governed by a star graph. In this situation, for given flee time, the computation of dwell-flee relations reduces to a minimax optimization problem.