Kanat Camlibel from the SCAA group was recently promoted to Full Professor in recognition of his achievements in research, teaching and administration.

# Category: SCAA

## SCAA colloquium: Teke Xu

**Title:**A non-linear model for the water hammer problem

**Abstract:**The water flow and water hammer in a pipe is usually modelled by Euler equations which consists of 2 partial differential equations. The classical PDEs are nonlinear and inhomogeneous, and according to the existing research so far, it can be simplified to a switched DAE or ODE system under some assumptions. The result in some literature shows that simplification works well and converges to the PDE model by numerical solutions. However, how they (PDE and ODE model) converge to each other in an analytical way, or the error between them has not been quantified, and my work is to close this gap. The main method is to divide the process into 3 parts: before the valve closes, when the valve closes and after the valve has been closed.

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

## SCAA colloquium: Alden Waters

**Title:** Analytic Properties of Heat Equation Solutions and Reachable Sets

**Abstract:** We consider heat equations on bounded Lipschitz domains Omega in R^d and show that solutions to the heat equation for positive times are analytically extendable to a subdomain of the complex plane containing Omega. Our analysis is based on the boundary layer potential method for the heat equation. In particular, our method gives an explanation for the shapes appearing in the literature in 1d, which is not so easy to explain using Fourier analysis alone. I will also discuss the converse theorem, namely that certain sets in the complex plane can be realized as solutions to the heat equation on the boundary of Omega when Omega is a ball. Boundary layer potential theory also gives an indication that this statement is more difficult if Omega is not a ball. This exciting new technique to analyze the question of reachable sets is joint work with Alexander Strohmaier.

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

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## SCAA colloquium: Brayan Shali

**Title:**A contract theory for linear systems

**Abstract:**We introduce contracts for linear time-invariant systems with inputs and outputs. Contracts are used to express formal specifications on the dynamic behaviour of such systems through two aspects: assumptions and guarantees. The assumptions capture the available knowledge about the dynamic behaviour of the environment in which the system is supposed to operate. The guarantees capture the required dynamic behaviour of the system when interconnected with its environment. We also define and characterize notions of contract refinement and contract conjunction. The former allows one to compare contracts and the latter allows one to fuse the specifications expressed by multiple contracts. Finally, we also define and characterize notions of contract composition, which can be used to analyse and design interconnections of systems.

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

## SCAA colloquium: Ashish Cherukuri

*This talk has been cancelled.*

## SCAA colloquium: Alden Waters

*This talk has been cancelled.*

## 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.

## 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.

## Restart of SCAA Colloquium

After a long break we are happy to announce that the regular SCAA colloquia will resume starting this week. The first talk will be given by Sutrisno.