Rational representations and behavioral distance

PhD ceremony: Mr. V.S. Gottimukkala, 11.00 uur, Academiegebouw, Broerstraat 5, Groningen

Dissertation: Rational representations and behavioral distance

Promotor(s): prof. H.L. Trentelman

Faculty: Mathematics and Natural Sciences

In this thesis, we have solved a number of problems related to modeling, analysis and control of dynamical systems. In order to do so, we use an elegant mathematical approach called the "behavioral approach". A dynamical system is determined uniquely by its behavior which is the set of trajectories that satisfy the physical laws that govern the system. We have dealt with a special class of dynamical systems called linear differential systems. A behavior of a linear differential system admits many different kinds of representations. We are primarily interested in rational representations of behaviors in this thesis. As the first problem, we have solved the issue of the equivalence of rational representations of behaviors. Further, we have dealt with in detail how (minimal) state representations and rational representations of a given behavior are related. We have introduced several notions of behavioral distance using the concept of gap metric. We have compared the values and topologies associated with these notions of distance, and also have expressed them in terms of rational representations as well as state representations. Finally, using these concepts of distance, we have solved the problem of robust stabilization of linear systems by defining the neighborhoods around the nominal plant in a representation free way.