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 the Lyapunov Function

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

$V(x)-\epsilon x^{T}x\geq 0$

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

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.

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Local Lyapunov Search