LMIs in Control/pages/LMI for Minimizing Condition Number of Positive Definite Matrix

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LMIs in Control/pages/LMI for Minimizing Condition Number of Positive Definite Matrix


The System:[edit]

A related problem is minimizing the condition number of a positive-defnite matrix that depends affinely on the variable , subject to the LMI constraint > 0. This problem can be reformulated as the GEVP.

The Optimization Problem:[edit]

The GEVP can be formulated as follows:


minimize

subject to > 0;

>0;

< < .

We can reformulate this GEVP as an EVP as follows. Suppose,

= + , = +


The LMI:[edit]

Defining the new variables = , = we can express the previous formulation as the EVP with variables and :

miminize

subject to + >0; < + <

Conclusion:[edit]

The LMI is feasible.

Implementation[edit]

References[edit]