= Jan C. Willems
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\b[Jan C. Willems] was an electrical engineer and systems theorist whose work helped make <dissipativity (control theory)> a general tool for studying <dynamical systems>. His university-hosted curriculum records an electrical-engineering doctorate at MIT in1968, a systems-and-control professorship at Groningen from1973, and later work as a guest professor at KU Leuven. It records his death on31August2013.<Curriculum Vitae of Jan C. Willems>[Professional biography]{ref}
\Image[https://homes.esat.kuleuven.be/~sistawww/smc/jwillems/Photos/photo1.jpg]
{title=Jan C. Willems, portrait linked from his university homepage}
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His1972general theory expresses a system's balance using a <storage function> and <supply rate>. The formulation compares a change in stored quantity with integrated input supply, allowing physical <energy> accounting and input–output performance bounds to share one mathematical language.<Dissipative Dynamical Systems, Part I: General Theory by Jan C. Willems>[Part I: General Theory, storage and supply formulation]{ref}
An original example illustrates the scientific idea. A2kilogram mass with viscous coefficient3newton-seconds per metre obeys $2\dot v=u-3v$. Its <kinetic energy> is $S=v^2$ joules when $v$ is expressed in metres per second, and
$$
\dot S=uv-3v^2\leq uv.
$$
At constant <velocity>1metre per second, a3newton <force> supplies3watts, all dissipated while the stored <kinetic energy> stays1joule. The <dissipativity (control theory)> article develops the general inequality; this simple case shows why its supply and storage terms must be distinguished.
Willems also developed <behavioral systems theory>, which describes a <dynamical system> by a family of admissible time histories. His curriculum explains the motivation: an interconnected system need not come with a uniquely privileged division into <control inputs> and <plant outputs>. Interconnection can instead impose shared variables and compatibility between trajectories.<Curriculum Vitae of Jan C. Willems>[Professional biography, behavioral approach and interconnection]{ref} The two contributions address complementary questions: which histories are possible, and what balance law must each history obey?
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