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The dissipativity concept sits at the intersection of physics, systemstheory, and control engineering, as a natural generalisation of passive systemsthat dissipate energy. It relates the external behavior of systems to theirinternal state, and connects the subjects of optimal control, algebraic Riccatiequations, linear matrix inequalities, complex functions, and spectralfactorization. Within control, its applications include the analysis and designof interconnected systems (such as cyber-physical systems), robustness, and theabsolute stability problem, and network synthesis (of electrical, mechanical,and multi-physics systems).  This article details recent developments in the treatment of dissipativityand the related concept of reciprocity for systems that are not necessarilycontrollable and need not lend themselves naturally to an input-state-outputperspective, as is the case for many physical and passive systems. Weillustrate these concepts using simple electric circuit and mechanical networkexamples.

Dissipativity, reciprocity and passive network synthesis: from Jan Willems' seminal Dissipative Dynamical Systems papers to the present day