Contributions to the analysis of structural properties of dynamical systems in control and systems theory

The importance of differential geometric methods in system analysis has grown immensely over the last decades. One of the reasons for this is the fact that the geometric language offers the possibility to comprise difficult mathematical, physical and system theoretical problems in an elegant and concise manner, which additionally allows for an intrinsic description that is not dependent on the chosen coordinates. The desire to classify systems either with respect to the structure of the equations and/or with respect to the physical background can be handled using geometric tools in a remarkable way - this is the main motivation for this work. In this monograph we first present some selected topics of geometric systems theory. Subsequently, we address the problem of triangulations of nonlinear multi-input systems, which is connected to the question of what a normal form for flat systems that are not linearizable by static feedback could look like. This question will be analyzed by means of exterior algebra by using a Pfaffian system representation. This second part is concerned with structural properties of the system equations for finite-dimensional systems and in the third part we focus on the physical properties that lead to a structural classification for infinite-dimensional systems described by partial differential equations. Here, systems that can be derived by means of a variational principle will be analyzed and their reinterpretation in a port-Hamiltonian framework will play a prominent role.