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LMIs in Control/Click here to continue/Controller synthesis/Quadratic Polytopic Stabilization

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

The System

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

where ,, and

The Data

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The matrices necessary for this LMI are , , and

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

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There exists a K such that

is quadratically stable for if and only if there exists some P>0 and Z such that

Conclusion:

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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

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

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Quadratic Polytopic Controller
Quadratic Polytopic Controller

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