Lecturer

Undergraduate course, University of Groningen, Faculty of Science and Engineering, 2020

I was a lecturer, together with Prof. Stephan Trenn, of the course “Advanced Systems Theory” for bachelor students of Applied Mathematic at University of Groningen.

Course description:

This course deals with linear input-output systems in state space form. The course starts with a review of the most important concepts on linear systems that were already taught in the first year course Linear Systems. We review the notions of internal and external stability, controllability and observability with special emphasis on their geometric characterizations. We also review the notions of stabilizability and detectability and discuss their relevance in the design of stabilizing controllers and observer design. We then shift to systems with disturbance inputs, and formulate the design problem of disturbance decoupling by state feedback. We give necessary and sufficient conditions for solvability of this problem in terms of controlled invariant subspaces. Next, we consider the more general formulations of these problems where only part of the state is available for feedback. In this case we are forced to apply dynamic output feedback, and the solution of the decoupling problems in addition uses the concepts of conditioned invariant and detectability subspaces. We also discuss the classical problem of tracking and regulation that requires the design of dynamic controllers such that the output of the controlled system asymptotically follows a given time signal, despite the fact that the systems is affected by external disturbances. This problem is studied by means of solvability of linear matrix equations. As a final subject, we consider linear networked multi-agent systems, which deals with controlling (possibly large numbers of) interconnected linear input-output systems. The interconnection structure of such networks are described by graphs, representing the communication between the agents. We discuss the notions of consensus and synchronization for such systems, and study under what conditions controllers exist that achieve consensus.