SCAA colloquium: Arjan van der Schaft


16:00 - 17:00


Title: Cyclo-dissipativity Revisited

Abstract: Dissipativity theory of nonlinear systems originates from the seminal paper 1972 of Jan Willems. It unifies classical input-output stability theory, centered around the passivity and small-gain theorems, with Lyapunov function theory for autonomous dynamical systems. In particular, it aims at deriving Lyapunov functions for large-scale interconnected systems, based on the knowledge of the component systems, and the way they are coupled to each other. Furthermore, it directly relates to physical systems theory, network synthesis, and optimal control. The more general notion of cyclo-dissipativity, as first formulated in a somewhat forgotten paper by Jan Willems in 1973, originally aimed at extending stability analysis based on dissipativity towards instability theorems. It was further explored in an unpublished technical report by David Hill and Peter Moylan in 1975. Since then the notion of cyclo-dissipativity has not received much detailed attention, although implicitly it was used as the basic dissipativity notion in linear behavioral theory. In this talk we will revisit the notion of dissipativity and cyclo-dissipativity, by unifying earlier definitions and developments. This will turn out to be instrumental for developing a more complete theory, including external characterization and description of the set of (indefinite) storage functions. Finally, the developed theory will be illustrated on the formulation of the Clausius inequality in thermodynamics.

The colloquium will take place online in Google Meet. You can email the organizer for a link to the meeting.

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