Computational complexity in robust controller synthesis

This paper is concerned with the computational complexity analysis in robus t control problems. We first formulate a fairly general class of nonconvex optimization problem named "Matrix Product Eigenvalue Problem (MPEP)" and e xplain the connection to robust control problems. We next summarize the wor st case computational complexity results and investigate the computational cost for the actual case. Finally, we make a comparison with an element-wis e bounding for the BMI optimization problem and a matrix-based bounding for the MPEP.