## Christopher Kellett (06/07/17)

Math Colloquium

### Speaker: Christopher Kellett, University of Newcastle (Australia)

### Title: Back and Forth in Lyapunov’s Second Method: Non-Uniform Subtleties

Location: Tg-227 (Tæknigarður, 2. hæð)

Time: Thursday 6 July at 13:20

### Abstract:

Lyapunov’s second or direct method provides an easy-to-check sufficient condition for stability properties of equilibria. The converse question – given a stability property, does there exist an appropriate Lyapunov function? – has been fundamental in differentiating and classifying different stability properties, particularly with regards to “uniform” stability.

In this talk, I will review the usual textbook definitions for Lyapunov functions for time-varying systems and describe where they are deficient. Some interesting new sufficient (and probably necessary) conditions pop up along the way.