Stability of Linear Systems

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Notebook Content¶

This notebook explores the Lyapunov equation and stability of linear systems.

Again, we use the linearized pendulum dynamics as an example, and design a proportional-derivative (PD) controller and assess the performance using the Lyapunov equation.

$\dot{\theta}=\phi$ $\dot{\phi}=-\frac{g}{\ell}\sin(\theta)$

Info

You will need to make sure you append to your path the directory where you have the notebooks and utils folder so that you can use the utils functions in ‘_547utils.py’. You may also want to install seaborn for nice plotting style.