Lecture 5

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In this lecture we introduce Lyapunov functions, and explain how they can be used to analyse nonlinear systems. By the end of this lecture you should be able to:

  • Introduce mathematical background used for Lyapunov stability analysis
  • Prove stability of simple systems using Lyapunov's method.

The lecture slides can be downloaded here: lec04.pdf

The note we took in class can be downloaded here: FRTN05_Lecture05_annotated.pdf

Recommended reading: Glad & Ljung Ch. 12.2, Khalil Ch. 4.1-4.3

What is a Lyapunov function

We introduce the concept of a Lyapunov function.

Lyapunov's method

We explain how to use Lyapunov functions to investigate stability of equilibrium points.

Example

We illustrate Lyapunov's method on a simple example.

Lyapunov's linearisation method

 

 

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