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LMIs in Control/Tools/Matrix Norm Minimization
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The System
Note that are symmetric matrices.
The Data
The Optimization Problem
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 Matrix
Mathematical description of the LMI formulation:
Conclusion:
This problem is a slight generalization of the eigenvalue minimization problem for a matrix.
are parameters to be optimized
Implementation
A link to Matlab codes for this problem in the Github repository:
https://github.com/asalimil/LMI-for-Matrix-Norm-Minimization
Related LMIs
LMI for Matrix Norm Minimization
LMI for Schur Stabilization
External Links
A list of references documenting and validating the LMI.
- LMI in Control Systems Analysis, Design and Applications
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