LMi for Minimizing Eigenvalues of a Matrix

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LMi for Minimizing Eigenvalues of a Matrix

The System[edit]

Note that are symmetric matrices.

The Data[edit]

The Optimization Problem[edit]

Find

to minimize,

According to Lemma 1.1 in [1] page 10, the following statements are equivalent

The LMI: The Lyapunov Inequality[edit]

Title and mathematical description of the LMI formulation.

Conclusion:[edit]

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-Minimizing-the-Maximum-Eigenvalue-of-Matrix/blob/master/README.md

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

Return to Main Page:[edit]