Midway Evaluation in Mathematics - Stefanía Andersen Aradóttir

Title of thesis:
This and that on Lyapunov functions: Quadratic functions, linear programming, and minimum average dwell time.

Student:
Stefanía Andersen Aradóttir

Doctoral committee:
Dr. Sigurður Freyr Hafstein, Professor of Mathematics at the University of Iceland
Dr. Anna Soffía Hauksdóttir, Professor of Electrical Engineering at the University of Iceland
Dr. Elias August, Associate Professor of Electrical Engineering at Reykjavik University
Dr. Peter Giesl, Professor of Mathematics at the University of Sussex, UK

Abstract:
Lyapunov functions have been utilized to study the stability of switched linear systems, both with and without dwell time constraints on the switching signal. Within the field of control theory, symmetric and positive definite matrices are commonly used to represent quadratic functions, and linear matrix inequalities (LMIs) are typically employed for numerical computations of quadratic Lyapunov functions. This lecture will cover how the nonlinear constraints associated with the use of LMIs can be replaced with linear ones, enabling the use of linear programming to compute a piecewise quadratic common Lyapunov function. It will also discuss how minimum average dwell time constraints impact the problem formulation.