# LMIs in Control/pages/Quadratic polytopic stabilization

< LMIs in Control | pages

A Quadratic Polytopic Stabilization Controller Synthesis can be done using this LMI, requiring the information about , , and matrices.

**The System**Edit

where , , at any .

The system consist of uncertainties of the following form

where , , and

**The Data**Edit

The matrices necessary for this LMI are , , and

**The Optimization and LMI:**LMI for Controller Synthesis using the theorem of Polytopic Quadratic StabilityEdit

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

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

This implementation requires Yalmip and Sedumi. https://github.com/JalpeshBhadra/LMI/blob/master/quadraticpolytopicstabilization.m

**Related LMIs**Edit

Quadratic Polytopic Controller

Quadratic Polytopic Controller

**External Links **Edit

- 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.