LMIs in Control/pages/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[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]

Quadratic Polytopic Controller
Quadratic Polytopic Controller

External Links [edit | edit source]