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LMIs in Control/pages/LMIforMinimizingMatrixNorm
Reference material by Wikibooks contributors. This retains its source identity and is not 411 news reporting.
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: LMI for matrix norm minimization
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 Eigenvalue Minimization
External Links
A list of references documenting and validating the LMI.
- LMI in Control Systems Analysis, Design and Applications
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