Jan Camiel Willems (18 September 1939 – 31 August 2013) was a Belgian mathematical system theorist who has done most of his scientific work while residing in the Netherlands and the United States. He is most noted for the introduction of the notion of a dissipative system and for the development of the behavioral approach to

systems theory Systems theory is the interdisciplinary study of systems, i.e. cohesive groups of interrelated, interdependent components that can be natural or human-made. Every system has causal boundaries, is influenced by its context, defined by its structu ...

Biography

Jan Willems was born in

Bruges Bruges ( , nl, Brugge ) is the capital and largest City status in Belgium, city of the Provinces of Belgium, province of West Flanders in the Flemish Region of Belgium, in the northwest of the country, and the sixth-largest city of the countr ...

in 1939. He studied engineering at the

University of Ghent Ghent University ( nl, Universiteit Gent, abbreviated as UGent) is a public research university located in Ghent, Belgium. Established before the state of Belgium itself, the university was founded by the Dutch King William I in 1817, when the ...

, obtained the M.Sc. degree from the

University of Rhode Island The University of Rhode Island (URI) is a public land-grant research university with its main campus in Kingston, Rhode Island, United States. It is the flagship public research as well as the land-grant university of the state of Rhode Island ...

, and the Ph.D. degree from the

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the ...

electrical engineering Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the l ...

in 1968. He was an assistant professor in the Department of

Electrical Engineering Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the l ...

at MIT from 1968 to 1973. On 1 February 1973 he was appointed Professor of Systems and Control in the Mathematics Department of the

University of Groningen The University of Groningen (abbreviated as UG; nl, Rijksuniversiteit Groningen, abbreviated as RUG) is a Public university#Continental Europe, public research university of more than 30,000 students in the city of Groningen (city), Groningen in ...

. In 2003 he became

emeritus professor ''Emeritus'' (; female: ''emerita'') is an adjective used to designate a retired chair, professor, pastor, bishop, pope, director, president, prime minister, rabbi, emperor, or other person who has been "permitted to retain as an honorary title ...

. Afterwards, he became Guest Professor at the

KU Leuven KU Leuven (or Katholieke Universiteit Leuven) is a Catholic research university in the city of Leuven, Belgium. It conducts teaching, research, and services in computer science, engineering, natural sciences, theology, humanities, medicine, l ...

. He served terms as chairperson of the European Union Control Association and of the Dutch Mathematical Society (Wiskundig Genootschap). He was managing editor of the SIAM Journal of Control and Optimization and as founding and managing editor of Systems & Control Letters.

Research contributions

In his Ph.D. dissertation, Willems worked on input/output stability. In an often-cited 1972 paperJ. C. Willems. ''Dissipative dynamical systems – Part I: General theory, Part II: Part II: Linear systems with quadratic supply rates '', Volume 45, pages 321–351 and 352–393, 1972. Available online http://homes.esat.kuleuven.be/~jwillems/Articles/JournalArticles/1972.1.pdf. he introduced the notion of a ''dissipative system''. This notion is a generalization of

Lyapunov function In the theory of ordinary differential equations (ODEs), Lyapunov functions, named after Aleksandr Lyapunov, are scalar functions that may be used to prove the stability of an equilibrium of an ODE. Lyapunov functions (also called Lyapunov’s se ...

to input/state/output systems. The construction of the storage function, as the analogue of a Lyapunov function is called, led to the study of the

linear matrix inequality In convex optimization, a linear matrix inequality (LMI) is an expression of the form : \operatorname(y):=A_0+y_1A_1+y_2A_2+\cdots+y_m A_m\succeq 0\, where * y= _i\,,~i\!=\!1,\dots, m/math> is a real vector, * A_0, A_1, A_2,\dots,A_m are n\times n ...

(LMI) in

control theory Control theory is a field of mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a ...

. Applied to linear-quadratic-Gaussian control, the construction of the storage function leads to the

Kalman–Yakubovich–Popov lemma The Kalman–Yakubovich–Popov lemma is a result in system analysis and control theory which states: Given a number \gamma > 0, two n-vectors B, C and an n x n Hurwitz matrix A, if the pair (A,B) is completely controllable, then a symmetric matrix ...

. In the 1980s Willems worked on the geometric theory of linear systems, where he introduced the notion of almost invariant subspace. Since the 1990s, he has devoted his interest to the development of the behavioral approach to systems theory and control.J. Polderman and J. C. Willems. ''Introduction to Mathematical Systems Theory''. Springer-Verlag, New York, 1998. Available online http://wwwhome.math.utwente.nl/~poldermanjw/onderwijs/DISC/mathmod/book.pdf.J. C. Willems. The behavioral approach to open and interconnected systems: Modeling by tearing, zooming, and linking. ''Control Systems Magazine'', 27:46–99, 2007. Available online http://homes.esat.kuleuven.be/~jwillems/Articles/JournalArticles/2007.1.pdf. In the behavioral approach a dynamical system is simply viewed as a family of trajectories. This approach avoids having to separate the system variables into inputs and outputs.

Awards and honors

Willems was a fellow of the

IEEE The Institute of Electrical and Electronics Engineers (IEEE) is a 501(c)(3) professional association for electronic engineering and electrical engineering (and associated disciplines) with its corporate office in New York City and its operation ...

, the

Society for Industrial and Applied Mathematics Society for Industrial and Applied Mathematics (SIAM) is a professional society dedicated to applied mathematics, computational science, and data science through research, publications, and community. SIAM is the world's largest scientific socie ...

, the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

and

International Federation of Automatic Control The International Federation of Automatic Control (IFAC), founded in September 1957, is a multinational federation of 49 national member organizations (NMO), each one representing the engineering and scientific societies concerned with automatic c ...

. In 1998 he was an Invited Speaker of the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rename ...

in Berlin. In 1998, he received the

IEEE Control Systems Award The IEEE Control Systems Award is a technical field award given to an individual by the Institute of Electrical and Electronics Engineers (IEEE) "for outstanding contributions to control systems engineering, science or technology". It is an IEE ...

"for seminal contributions to control theory and leadership in systems research". In 2010, he became doctor

honoris causa An honorary degree is an academic degree for which a university (or other degree-awarding institution) has waived all of the usual requirements. It is also known by the Latin phrases ''honoris causa'' ("for the sake of the honour") or ''ad hono ...

of the

University of Liège The University of Liège (french: Université de Liège), or ULiège, is a major public university of the French Community of Belgium based in Liège, Wallonia, Belgium. Its official language is French. As of 2020, ULiège is ranked in the 301 ...

Selected publications

References

External links

Jan Willems' homepage
* S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan
Linear Matrix Inequalities in System and Control Theory
(book in pdf) {{DEFAULTSORT:Willems, Jan Camiel 1939 births 2013 deaths Belgian mathematicians Control theorists Ghent University alumni University of Rhode Island alumni MIT School of Engineering alumni MIT School of Engineering faculty Academic staff of the University of Groningen Fellows of the American Mathematical Society Fellows of the Society for Industrial and Applied Mathematics Fellow Members of the IEEE Scientists from Bruges Fellows of the International Federation of Automatic Control