LMIs in Control/pages/LMI for Matrix Norm Minimization

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LMIs in Control/pages/LMI for Matrix Norm Minimization

The System[edit | edit source]

Note that are symmetric matrices.

The Data[edit | edit source]

The Optimization Problem[edit | edit source]


to minimize,

According to Lemma 1.2 in [1] page 11, the following statements are equivalent

The LMI: Minimization of Maximum Eigenvalue of a Matrix[edit | edit source]

Mathematical description of the LMI formulation:

Conclusion:[edit | edit source]

This problem is a slight generalization of the eigenvalue minimization problem for a matrix.

are parameters to be optimized

Implementation[edit | edit source]

A link to Matlab codes for this problem in the Github repository:


Related LMIs[edit | edit source]

LMI for Matrix Norm Minimization

LMI for Schur Stabilization

External Links[edit | edit source]

A list of references documenting and validating the LMI.

  • [1] - LMI in Control Systems Analysis, Design and Applications

Return to Main Page:[edit | edit source]