Dwell‐time‐based stabilization of switched positive systems with unstable subsystems and destabilizing switchings

Abstract The exponential stabilization (ES) problem of switched positive systems is studied with dwell‐time switching under assumption that all subsystems can be unstable. Sufficient conditions on ES under dwell‐time switching are proposed by multiple time‐varying copositive Lyapunov functions. The main idea to achieve ES is to confine the dwell time, restrict the growth of the Lyapunov function of the active subsystem, and evaluate the ratio of stabilizing switchings to compensate the state divergence arising from either destabilizing switchings or unstable subsystems. Two examples are given to show our approaches.