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PhD Defence by Tobias Leth


19.12.2017 kl. 13.00 - 19.12.2017 kl. 16.00


“Polynomials in the Bernstein Basis and Their Use in Stability Analysis”

The thesis “Polynomials in the Bernstein Basis and Their Use in Stability Analysis” considers stability analysis of polynomial dynamical systems using formulations in the Bernstein basis. The thesis covers notation and definitions used to introduce and utilize the Bernstein basis. The basis is then used for positivity certification and it is used in the derivation of numerical methods for automated synthesis of Lyapunov functions. The derived linear programming problems are often infeasible and a novel application of Farkas’ Lemma is utilised to modify the problems into being solvable. The algorithms are implemented as a software toolbox for MatLab.

In this presentation, focus is to convey the concepts of the thesis and to explain it to people without expert knowledge on the subjects. The challenges overcome in the thesis are exemplified and care will be taken for the presentation to be of value for people in academia as well as for people outside academia. Some aspects of the thesis are left out to make room for a thorough treatment of the core elements of the challenges and solutions.

Assessment Committee
Associate Professor Raphaël Jungers, ICTEAM Institute, (UCLouvain), Belgium
Software Engineer Joachim Dahl, Mosek ApS, Denmark
Associate Professor Henrik Schiøler, Aalborg University, Denmark (chairman)

Professor Rafal Wisniewski, Aalborg University, Denmark

Associate Professor Christoffer Sloth, previously Aalborg University, now SDU, Denmark

Associate Professor Jan Dimon Bendtsen, Aalborg University, Denmark

After the defence there will be a reception at Fredrik Bajers Vej 7, C3-203


Free of charge


Automation and Control Section, Department of Electronic Systems


Aalborg University, Fredrik Bajers Vej 7, B3-104

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