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

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.

ImplementationEdit

ReferencesEdit