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