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LMIs in Control/Click here to continue/Fundamentals of Matrix and LMIs/LMI for Minimizing Condition Number of Positive Definite Matrix
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The System:
A related problem is minimizing the condition number of a positive-definite matrix that depends affinely on the variable , subject to the LMI constraint > 0. This problem can be reformulated as the GEVP.
The Optimization Problem:
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:
Defining the new variables = , = we can express the previous formulation as the EVP with variables and :
miminize
subject to + >0; < + <
Conclusion:
The LMI is feasible.
Implementation
References
LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.