LMIs in Control/pages/LMI for Matrix Norm Minimization

LMIs in Control/pages/LMI for Matrix Norm Minimization

The SystemEdit

 

Note that   are symmetric matrices.

The DataEdit

 

The Optimization ProblemEdit

Find

 

to minimize,

 

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

 

The LMI: Minimization of Maximum Eigenvalue of a MatrixEdit

Mathematical description of the LMI formulation:

 

Conclusion:Edit

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

  are parameters to be optimized

ImplementationEdit

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

https://github.com/asalimil/LMI-for-Matrix-Norm-Minimization

Related LMIsEdit

LMI for Matrix Norm Minimization

LMI for Schur Stabilization

External LinksEdit

A list of references documenting and validating the LMI.

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

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