## Obituaries: Christopher Byrnes

**December 14, 2010**

Christopher Byrnes, 1949–2010

Christopher Byrnes was born in the Bronx, New York, on June 28, 1949. He received a bachelor's degree in mathematics from Manhattan College in 1971, and master's and doctoral degrees in mathematics from the University of Massachusetts, Amherst, in 1973 and 1975. After an instructorship at the University of Utah (1975–78), he became an assistant and then associate professor in the Division of Applied Science at Harvard University (1978–84), followed by a move to Arizona State University as a research professor of engineering and mathematics (1984–89). In 1989, he joined the faculty of Washington University as chair and professor in the Department of Systems Science and Mathematics, where he was subsequently named to the Skinner Professorship. Under his leadership as dean of the School of Engineering & Applied Science, a position he held from 1991 to 2006, the school's endowment increased from $54 million to $185 million and the number of endowed professorships from nine to 37.

In addition to Stockholm, Chris held many visiting appointments in the course of his career, at universities in Paris, Rome, Kiev, Moscow, Tokyo, Groningen, and Bremen, among others. At the time of his death, he was also a research professor at North Carolina State University. Chris was a gifted teacher who had 20 PhD students, a number of whom currently hold prestigious positions at major universities in the United States and Europe.

Chris was the author of more than 250 technical papers and books, and his contributions to mathematics and engineering spanned a wide range of topics, from partial differential equations to algebraic geometry to control theory. He had an almost encyclopedic knowledge of large portions of mathematics, and he brought deep mathematical insight and a plethora of advanced mathematical tools to tackle important and difficult problems in systems and control theory. A Fellow of the IEEE, he was a two-time recipient of the IEEE Control Systems Society's George Axelby Prize and, in 2008, of its Hendrik W. Bode Prize for fundamental contributions to algebraic and geometric approaches to systems and control; in 1993, he received an

*Automatica*Best Paper Award from the International Federation for Automatic Control. SIAM recognized his contributions to control theory and differential equations by awarding him the W.T. and Idalia Reid Prize in 2005, and in 2009 made him a member of the inaugural class of SIAM Fellows.

Among his research interests were feedback design in automatic control, nonlinear dynamics and control, and statistical estimation and filtering. His research found application in electrical power systems, signal processing, and speech synthesis, among other areas. He held four U.S. patents and received more than $5 million in competitively awarded grants. Those of us who had the privilege of working closely with Chris can attest to the power of his mind and the generosity of his spirit. He was a gifted collaborator and a wonderful person with whom to share ideas. What follows are more specific remarks about the nature and impact of his work, summarized from comments by a few of his many collaborators.

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Chris was a major contributor in the analysis and design of nonlinear control systems. Problems in which his ideas played a fundamental role and paved the way for a series of advances include a nonlinear enhancement of the theory of output regulation in the late 1980s; this work eventually led to the nonlinear regulator equations and to the concept of internal models for nonlinear systems. Moreover, his ideas were instrumental in the development of the concept of steady-state behavior of a nonlinear system and problems associated with shaping the response of the system. In the early 2000s, Chris described how ideas from the attractor theory of dynamical systems can provide an appropriate paradigm for a general, non-equilibrium-based approach to systems.

In the mid-1980s Chris turned his attention to distributed parameter systems, where his first efforts with subsequent longtime collaborator and co-author David Gilliam were directed toward the extension of feedback design methods from classic automatic control to the infinite-dimensional setting. This led to a study of root-locus design methods for distributed parameter systems; the result was a new interpretation of zero dynamics for boundary control systems that influenced much of the later work of Chris and his co-authors. While the usual definitions of zeros and poles do not make sense for nonlinear systems, the notion of convergence of trajectories does. For certain boundary control systems governed by nonlinear partial differential equations, Chris and collaborators showed that closed-loop trajectories tend to trajectories of the open-loop zero dynamics as the gain parameters are increased to infinity.

Chris also extended his work on output regulation for finite-dimensional nonlinear systems to linear and nonlinear distributed parameter systems. Through the use of a center manifold theorem in infinite dimensions, he and several co-authors extended the geometric methods to include various classes of nonlinear distributed parameter systems.

Chris's most recent efforts were motivated by his interest in non-equilibrium output regulation and led to the development of the so-called zero dynamics inverse design method. This method is useful for obtaining a feedback compensation scheme that achieves asymptotic regulation for a wide class of linear and nonlinear problems.

Almost thirty years ago, Chris began what would be a long-term collaboration with Anders Lindquist to study the partial realization problem from a topological point of view. To this collaboration Chris brought deep mathematical insight and a wide array of advanced mathematical tools from algebra, algebraic geometry, topology, and differential geometry. This research led to a complete parameterization of the rational covariance extension problem and to a convex optimization approach to this problem.

Chris also applied his knowledge of nonlinear dynamics to investigations of the dynamical behavior of Kalman filtering algorithms. This work eventually led to a duality principle and a fast algorithm for Kalman filtering.

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On September 10 and 11, friends, colleagues, and former students celebrated Chris's life at a memorial workshop held in Lubbock, Texas, where Chris had a relationship of more than 30 years with Texas Tech faculty and students. With his wife, Renee, in attendance, the group offered warm memories and personal comments, as well as technical presentations.

A sampling of the tributes: "A remarkable man on many levels, a brilliant mathematician, a remarkable organizer, a funny raconteur and a loving father"; "an excellent mathematician who continued to do world-class research even while he was dean"; "he was full of ideas and seemed to have at his command every theorem in advanced mathematics, so much so that he could produce a detailed proof of any theorem at a moment's notice."

And an anecdote: "In Bremen, Chris was showing me a statue of the cock on a cat on a hound on a donkey in the town square. I asked Chris, ‘What is this statue all about?' He replied, ‘Let's go to a pub, and I'll tell you about it.' We didn't step into a tourist bar near the square, but he led me off the beaten path and down a narrow lane. There we entered a vibrant bar and were greeted by a large German lady who said, ‘Professor Byrnes, you've been gone too long.' What ensued was one of the most memorable happy hours I'll ever recall. I learned Budweiser was a Czechoslovakian beer and that the brewery in St. Louis obtained the name from the Czechoslovakians. I can remember the bar lady introducing me to ‘ein Viertel' (a quarter liter beer warm up). I found myself listening to an authority on the Brothers Grimm fairy tale "The Town Musicians of Bremen." Chris was amazing. It seemed as if anything he had ever learned he could immediately access from his vast memory file."---

*H.T. Banks, North Carolina State University, Raleigh, and David Gilliam, Texas Tech University, Lubbock, with contributions from Art Krener, Tony Bloch, and John Lund.*