SCAA colloquium: Jaap Eising

Title: On Duality for Lyapunov Functions of Nonstrict Convex Processes
Abstract: This talk introduces a novel definition of Lyapunov functions for difference inclusions defined by convex processes. This class of systems is particularly interesting due to its application in modeling linear systems with conic (e.g. nonnegativity) constraints. After introducing the notions of weak and strong Lyapunov functions we will present a theorem revealing a duality relation between them. This relation will relate in a natural way to the duality between (strong) stabilizability and (strong) detectability of linear systems.

SCAA colloquium: Arjan van der Schaft

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 It was further explored in an unpublished technical report by David Hill and Peter Moylan in 1975.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.

SCAA colloquium: Sutrisno Sutrisno

Title: Observability of Switched Linear Singular System in Discrete Time: Single Switch Case

Abstract: We investigate the observability of switched linear singular systems in discrete time. In this study, we restrict this system with a single switch switching signal. We provide a necessary and sufficient condition for observability for any switching time and for a switching time that is far enough from the initial time or final time. Some illustrative examples are discussed to illustrate the results.

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

Floris Takens Seminar: Alden Waters (online)

Speaker: Alden Waters (SCAA)

Abstract: We consider the problem of obstacle scattering for the Helmholtz equation with the p-form Laplace Beltrami operator. On manifolds which are asymptotically Euclidean we show resolvent expansions, and expansions for the scattering matrix. The key idea is the use of plane waves. We also give a cohomological interpretation of the scattered waves allowing us to identify geometric structures from afar. Joint work with F. Hanisch.

Watch the stream online at the given time. You can also join a Google Meet Room for this presentation, please contact the organizers to receive a corresponding link.