Jan C. Willems

Jan C. Willems was an electrical engineer and systems theorist whose work helped make dissipativity 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.^[ref]

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.^[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, andAt constant velocity1metre per second, a3newton force supplies3watts, all dissipated while the stored kinetic energy stays1joule. The dissipativity 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.^[ref] The two contributions address complementary questions: which histories are possible, and what balance law must each history obey?