CARMA Seminar

4:00 pm

Tuesday, 13th Jun 2017

V205, Mathematics Building

A/Prof Chris Kellett

(School of Electrical Engineering and Computer Science, The University of Newcastle)

Back and Forth in Lyapunov's Second Method - Non-uniform Subtleties

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.