User:Margav06/sandbox/Click here to continue/Applications of Non-Linear Systems/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 the Lyapunov Function
Find a polynomial (our Lyapunov function) $$V(x)$$, supposing there exists scalar $$\epsilon > 0$$ such that:

$$ V(x) -\epsilon x^Tx \geq 0 $$

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

Example
Code example in SOStools probably worthwhile!

Reference
SOS tools manual is a good one

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

Related LMIs
Add things here about SOS methods

Local Lyapunov Search