A Quadratic Polytopic Stabilization Controller Synthesis can be done using this LMI, requiring the information about , , and matrices.
where , , at any .
The system consist of uncertainties of the following form
where , , and
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
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.
External Links Edit