# 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

- LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.