Robust stabilization of switched linear systems via static state feedback and switching with dwell time

This paper addresses the robust stabilization of parametric uncertain switched linear systems with unstable subsystems and constrained switching with dwell time. First, sufficient conditions for asymptotic stabilization of the nominal switched linear systems via static state feedback gains and dwell time switching are proposed. Then, for the parametric uncertain switched linear systems, a theorem is given to design the collection of static state feedback gains, such that the closed loop switched system with dwell time is robustly asymptotically stable. Additionally, the proposed conditions will also be adopted to design the stabilizing state feedback gains for the cases with arbitrarily fast switching signals. The obtained results are based on the assumption that all the nominal subsystems are controllable. Numerical examples are also included to show the efficiency of the results.