Hypocoercivity and controllability in linear semi-dissipative ODEs and DAEs

A detailed analysis of the stability of dynamical systems of evolution equations (finite or infinite-dimensional) is still very problem dependent and computationally challenging, see [6, 18, 19, 27]. In view of these challenges it is important to use structural information of the dynamical system to characterize stability, asymptotic stability and the transient behavior. In this paper we consider these questions for two classes of finite-dimensional linear systems, although we have in mind to extend these results to the infinite-dimensional case and will do so for some examples. The first class are ordinary differential equations (ODEs) of the form

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