## Obituaries: Jan Willems

**December 2, 2013**

*Jan Willems, 1939–2013*

He will be deeply missed by his former students and his many collaborators and colleagues, in Groningen and around the world, in his beloved field of systems and control. Although he played a prominent role in shaping the field over an exceptionally long period, he was as happy talking to young scientists as to top scientists. His door was always open to all.

Jan Willems was born on September 18, 1939, in Bruges, Belgium. After finishing his studies in engineering at the University of Ghent, he moved to the United States, where he obtained an MSc in electrical engineering from the University of Rhode Island in 1965, and a PhD in electrical engineering from the Massachusetts Institute of Technology in 1968. His doctoral dissertation, on input/output stability, appeared as the monograph

*The Analysis of Feedback Systems*(MIT Press, 1971). From 1968 to 1973, as an assistant professor in the Department of Electrical Engineering at MIT, he made fundamental contributions to the subject of optimal control, in particular linear quadratic problems with indefinite cost and the associated algebraic Riccati equation. His ground-breaking papers "Least Squares Stationary Optimal Control and the Algebraic Riccati Equation" (

*IEEE Transactions on Automatic Control*, 1971), and "Dissipative Dynamical Systems, General Theory" and "Dissipative Dynamical Systems, Linear Systems with Quadratic Supply Rates" (

*Archive for Rational Mechanics and Analysis*, 1972) led to the notions of dissipative systems and linear matrix inequality, which are generally considered the main concepts and tools for analysis in robust control, for both linear and nonlinear systems.

In 1973, Jan was appointed professor in the Department of Mathematics at the University of Groningen in the Netherlands to set up the new specialization of Systems and Control. During this period he worked in subjects from differential games, realization theory, and physical systems. By the end of the 1970s his research interests had shifted, to a geometric approach to control and to problems of disturbance decoupling. The latter research area attracted considerable attention at the time. In the late 70s he introduced the notions of almost controlled invariant and almost conditioned subspaces, which made it possible to resolve problems of approximate disturbance decoupling by high-gain feedback and singular linear quadratic problems. During this time, Jan was a founder (with Roger Brockett) of the journal

*Systems and Control Letter*s, which first appeared in 1981; he was a managing editor of the journal from 1981 to 1994. From 1989 to 1993, he was editor-in-chief of

*SIAM Journal on Control and Optimization*.

In the early 80s, Jan became conscious of the limitations of input/output thinking as the framework for the analysis and synthesis of open and interconnected systems. This uneasiness eventually led him to develop what is called a behavioral approach, in which a dynamical system is simply viewed as a family of trajectories. This work also emphasizes the importance---in, for example, object-oriented modeling---of latent variables in addition to the manifest variables that are the model's main concern. In the behavioral setting, interconnection is viewed as variable sharing, and control is viewed as interconnection, with feedback as an important special case. The original ideas were introduced in an early paper in the Italian journal

*Ricerche di Automatica*. More extensive development followed in a three-part paper in

*Automatica*(1986 and 1987), for which he received an

*Automatica*outstanding paper award in 1988. An important resource for his behavioral ideas is also the textbook (co-authored with Jan Willem Polderman)

*Introduction to Mathematical Systems Theory: A Behavioral Approach*from 1998.

In 1998 Jan received the IEEE Control Systems Award and the

*IEEE Control Systems Magazine*Outstanding Paper Award for "300 Years of Optimal Control, from the Brachystochrone to the Maximum Principle" (co-authored with Hector Sussmann).

During his years in Groningen, Jan played an important role in the systems and control community within the Dutch universities. Drawing on his natural charm and skills in diplomacy and persuasion, he was one of the founders and (from 1986 to 1996) chairperson of the Dutch Network of Systems and Control. The main goal was a national graduate school that would offer courses in systems and control theory---an ambition that was realized. The network was the precursor of the Dutch Institute of Systems and Control, which was founded in 1995 and whose board Jan chaired from 1995 to 1999.

In 1993 Jan was the general chair of the European Control Conference, which was held in Groningen, and he served as president of the European Union Control Association from 1994 to 1996. From 1994 to 1996, he was president of the Dutch Mathematical Society.

In 2003, Jan Willems became an emeritus professor of the University of Groningen and moved to Antwerpen, Belgium. There he was warmly welcomed at K.U. Leuven as a guest professor in the Department of Electrical Engineering, part of the research group Signals, Identification, System Theory, and Automation.

After his formal retirement from Groningen, Jan remained active as ever, fruitfully collaborating with many colleagues and actively participating in conferences and workshops all over the world. Until very recently he was an active participant in the annual IEEE Conference on Decision and Control, enjoying conversations with old friends and colleagues, but also inspiring young researchers with suggestions and (usually) positive criticism. His unquenchable scientific energy is manifest in the nearly one hundred publications he co-authored after his official retirement. Many of these later publications show his very deep thinking, scientific maturity, and clear vision on the field of systems and control. An example is the paper "The Behavioral Approach to Open and Interconnected Systems," which appeared in

*IEEE Control Systems Magazine*in 2007.

It is hard to imagine a world without Jan Willems, even though the products of his scientific activity, his contributions in shaping the field of systems and control, and his influence on the scientific taste and thinking of his students will remain.---

*Harry Trentelman, University of Groningen.*