LMIs in Control/pages/Quadratic polytopic stabilization
A Quadratic Polytopic Stabilization Controller Synthesis can be done using this LMI, requiring the information about , , and matrices.
The System[edit | edit source]
where , , at any .
The system consist of uncertainties of the following form
where ,, and
The Data[edit | edit source]
The matrices necessary for this LMI are , , and
The Optimization and LMI:LMI for Controller Synthesis using the theorem of Polytopic Quadratic Stability[edit | edit source]
There exists a K such that
is quadratically stable for if and only if there exists some P>0 and Z such that
Conclusion:[edit | edit source]
The Controller gain matrix is extracted as
Note that here the controller doesn't depend on
- If you want K to depend on , the problem is harder.
- But this would require sensing in real-time.
Implementation[edit | edit source]
This implementation requires Yalmip and Sedumi. https://github.com/JalpeshBhadra/LMI/blob/master/quadraticpolytopicstabilization.m
Related LMIs[edit | edit source]
External Links [edit | edit source]
- LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
- LMI Properties and Applications in Systems, Stability, and Control Theory - A List of LMIs by Ryan Caverly and James Forbes.
- LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.