LMIs in Control/Tools/Matrix Norm Minimization
< LMIs in Control | Tools
LMIs in Control/Tools/Matrix Norm Minimization
The System edit
Note that are symmetric matrices.
The Data edit
The Optimization Problem edit
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
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
Implementation edit
A link to Matlab codes for this problem in the Github repository:
https://github.com/asalimil/LMI-for-Matrix-Norm-Minimization
Related LMIs edit
LMI for Matrix Norm Minimization
LMI for Schur Stabilization
External Links edit
A list of references documenting and validating the LMI.
- [1] - LMI in Control Systems Analysis, Design and Applications