 CARMA OANT SEMINAR
 Joint CARMA OANT and EECS Seminar
 Speaker: A/Prof Christopher Kellett, School of Electrical Engineering and Computer Science, The University of Newcastle
 Title: Converse Theorems in Lyapunov's Second Method and Constructive Methods: Part I
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: CARMA [ENQUIRIES]
 Time and Date: 10:00 am, Wed, 24^{th} Sep 2014
 Abstract:
More than 120 years after their introduction, Lyapunov's socalled First and
Second Methods remain the most widely used tools for stability analysis of nonlinear
systems. Loosely speaking, the Second Method states that if one can find an appropriate
Lyapunov function then the system has some stability property. A particular strength of
this approach is that one need not know solutions of the system in order to make definitive
statements about stability properties. The main drawback of the Second Method is the
need to find a Lyapunov function, which is frequently a difficult task.
Converse Lyapunov Theorems answer the question: given a particular stability property,
can one always (in principle) find an appropriate Lyapunov function? In the first installment
of this twopart talk, we will survey the history of the field and describe several such Converse
Lyapunov Theorems for both continuous and discretetime systems. In the second instalment
we will discuss constructive techniques for numerically computing Lyapunov functions.
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