LMIs in Control/Global Lyapunov Function Search for System with Polynomial Dynamics

[UNDER CONSTRUCTION] - CME

Find the global Lyapunov function for a system with known polynomial dynamics.

Required Data

The system dynamics to be tested in the form $\dot{x} = f (x)$ where $f (x)$ is a polynomial function of the states $x$ .

Find a polynomial (our Lyapunov function) $V (x)$ , supposing there exists scalar $ϵ > 0$ such that:

$V (x) - ϵ x^{T} x \geq 0$

$- \dot{V} (x) = - \nabla V (x)^{T} f (x) \geq 0$

Code example in SOStools probably worthwhile!

SOS tools manual is a good one

Tie in the reference from SOS tools? The Khalil one seems correct.

Add things here about SOS methods

Local Lyapunov Search