LMIs in Control/Click here to continue/Applications of Non-Linear Systems/Lyapunov Stability of a System With Polynomial Dynamics
[UNDER CONSTRUCTION] - CME
Find the local Lyapunov function for a system with known polynomial dynamics.
Required Data
[edit | edit source]The system dynamics to be tested in the form where is a polynomial function of the states .
A function or functions representing the local domain over which stability is to be determined, . Commonly this is a ball of specified radius such that . [Is this assuming P-Compactness of the set?]
Find the Lyapunov Function
[edit | edit source]Suppose there exists Lyapunov function , a scalar , and (where is the set of Sum-of-Squares polynomials, all of which are positive) such that:
The Lyaponov function, if it exists, will be positive and always decreasing over the desired set
Example
[edit | edit source]Code example in SOStools probably worthwhile!
Reference
[edit | edit source]SOS tools manual is a good one
Tie in the reference from SOS tools? The Khalil?
Related LMIs
[edit | edit source]Add things here about SOS methods
Global Lyapunov Search