Robust stability and robust stabilizability for periodically switched linear systems

摘要

In this paper, the problem of robust stability and robust stabilizability for periodically switched linear systems is studied. The stability radius involving structured perturbations acting on both coefficient matrices and switching moments is introduced and investigated. Some lower bounds for stability radii of periodically switched linear systems are provided. After that, we derive the notion of fast and slow stabilizability for these systems. Some characterizations for robust stabilizability under structured perturbations are established. Several examples are given to illustrate the obtained results.