GEOMETRY OF THE LIMIT SETS OF LINEAR SWITCHEDSYSTEMS

摘要

This paper is concerned with asymptotic stability properties of linear switched sys-tems. Under the hypothesis that all the subsystems share a nonstrict quadratic Lyapunov function, we provide a large class of switching signals for which a large class of switched systems are asymp-totically stable. For this purpose we define what we call nonchaotic inputs, which generalize the different notions of inputs with dwell time. Next we turn our attention to the behavior for possibly chaotic inputs. Finally, we give a sufficient condition for a system composed of a pair of Hurwitz matrices to be asymptotically stable for all inputs.