Interconnection and Approximation in Networks of Dissipative Systems: Addressing Topological Simplification

Abstract

Half a century ago, and a few years after receiving his Ph.D. degree in electrical engineering at the Massachusetts Institute of Technology, Jan Willems published articles on dissipative dynamical systems <xref ref-type="bibr" rid="ref30" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[30]</xref> , <xref ref-type="bibr" rid="ref31" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[31]</xref> . In retrospect, the conceptual thinking and elegant generalization of the basic physical properties behind the notion of dissipation can be viewed as a distinctive stage in the field of systems and control. These articles have sparked an impressive number of scientific and technological contributions in the field of systems theory, mathematical modeling, and control systems synthesis. Especially with the introduction of powerful numerical tools to solve matrix inequalities, the classical theory of dissipative systems has proved a strong, rich, and (above all) elegant conceptual and theoretical framework to solve a plethora of relevant problems in robust control, stabilization, and estimation. It is a pleasure to contribute to a volume on dissipative dynamical systems, 50 years after the publication of these seminal articles.