LMIs in Control/LMI Matrix Properties/Minimization of Maximum Eigenvalue of a Matrix
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LMIs in Control/LMI Matrix Properties/Minimization of Maximum Eigenvalue of a Matrix
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 1.1 in [1] page 10, the following statements are equivalent
The LMI: The Lyapunov Inequality
[edit | edit source]Title and mathematical description of the LMI formulation.
Conclusion:
[edit | edit source]are parameters to be optimized
Implementation
[edit | edit source]A link to Matlab codes for this problem in the Github repository:
Related LMIs
[edit | edit source]LMI for Matrix Norm Minimization
External Links
[edit | edit source]A list of references documenting and validating the LMI.
- [1] - LMI in Control Systems Analysis, Design and Applications