Doctoral Defense in Mathematics - Stefanía Andersen Aradóttir

Doctoral candidate:
Stefanía Andersen Aradóttir

Title of thesis:
Stability Analysis of Switched Linear Systems via Numeric Computations of Continuous Piecewise Affine and Continuous Piecewise Quadratic Lyapunov Functions

Opponents:
Dr. Shenyu Liu, Assistant Professor at School of Automation, Beijing Institute of Technology, China
Dr. Florian Rupp, Professor at the Shool of Mathematics and Computer Science, Kutaisi International University, Georgia

Advisor:
Dr. Sigurður Hafstein, Professor at the Faculty of Physical Sciences, University of Iceland

Other members of the doctoral committee:
Dr. Elias August, Associate Professor at the Department of Engineering, Reykjavík University
Dr. Anna Soffía Hauksdóttir, Professor at the Faculty of Electrical and Computer Engineering, University of Iceland
Dr. Peter Giesl, Professor at the Department of Mathematics, University of Sussex, United Kingdom

Chair of Ceremony:
Dr. Birgir Hrafnkelsson, Professor and Head of the Faculty of Physical Sciences, University of Iceland

Abstract:
In this dissertation we present numerical methods for computing continuous piecewise affine (CPA) and continuous piecewise quadratic (CPQ) Lyapunov functions via linear programming (LP) for switched linear systems. We discuss the application of these methods to both arbitrary switching signals and signals subject to average dwell-time (ADT) constraints. Further, we discuss the challenges of computing the minimum average dwell-time (MADT) and present a search algorithm for its computation. Finally, we discuss our approach to computing CPQ functions via LP, rather than semidefinite programming (SDP).

About the doctoral candidate:
Stefanía graduated with B.Sc. degrees in Electrical and Computer Engineering and Applied Mathematics in 2017 and 2022 respectively from the University of Iceland. She received her M.Sc. degree in Electrical and Computer Engineering in 2023, also from the University of Iceland.