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 SystemEdit

 

where  ,  , at any  .
The system consist of uncertainties of the following form

 

where  , ,  and  

The DataEdit

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.


ImplementationEdit

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

Related LMIsEdit

Quadratic Polytopic   Controller
Quadratic Polytopic   Controller

External Links Edit