where and depend affinely on parameter .
The matrices .
The Optimization Problem:Edit
Solve the following semi-definite program
where is the controllability Gramian, i.e., .
The Hanakel norm (i.e., the square root of the maximum eigenvalue) of is less than if and only if the above LMI holds and the value function returns the maximum provable Hankel norm.
is assumed to be zero.
- LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
- LMI Properties and Applications in Systems, Stability, and Control Theory - A List of LMIs by Ryan Caverly and James Forbes.
- LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.