Automatic Control

Faculty of Engineering, LTH

Automatic Control

Lyapunov stability: Why uniform results are important, and how to obtain them


From: 2019-01-16 10:30 to: 11:15
Place: Seminar room - M2112B
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Typically when proving stability of a nonlinear dynamical system, one can find a Lyapunov function candidate of which the time-derivative along solutions is not negative definite, but only negative semi-definite. Often, the Lemma of Barbalat is used to complete the proof and show asymptotic stability. Though this approach works to show asymptotic stability, it does not yield uniform asymptotic stability, which from a robustness point of view is important, as will be illustrated by means of an example.

An alternative way to complete the proof is by usings Matrosov’s Theorem, or one of its generalisations. In addition to the Lyapunov function, auxiliary functions need to be found to complete the proof. We will present candidates for these auxiliary  functions that often work to complete a stability proof and show uniform asymptotic stability.

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