标题： Hurwitz系统的混合匹配 显示英文标题

标题： The hybrid matching of Hurwitz systems

摘要： 本文研究了由两个稳定线性系统组成的平面混合系统，这两个系统由Hurwitz矩阵定义，并且具有可以是分段线性、多项式或解析函数的跳跃。我们为这类混合系统的渐近稳定性提供了显式的解析必要和充分条件。我们还证明了这类混合系统中极限环的存在性。我们的结果可以看作是对已有文献中结果的推广。这得益于分段光滑向量场在混合结构中的嵌入。 显示英文摘要

摘要： In this paper we study planar hybrid systems composed by two stable linear systems, defined by Hurwitz matrices, in addition with a jump that can be a piecewise linear, a polynomial or an analytic function. We provide an explicit analytic necessary and sufficient condition for this class of hybrid systems to be asymptotically stable. We also prove the existence of limit cycles in this class of hybrid systems. Our results can be seen as generalizations of results already obtained in the literature. This was possible due to an embedding of piecewise smooth vector fields in a hybrid structure.