The matrix product eigenvalues problem - global optimization for the spectral radius of a matrix product under convex constraints

This paper defines a certain class of nonconvex optimization problems for robust control synthesis called the matrix product eigenvalues problem (MPEP), and minimizes the spectral radius of the product of two block-diagonal positive definite symmetric matrices under convex constraints. Many fixed order controller synthesis problems including performance and robustness specifications can be formulated as the MPEP. The purpose of this paper is to provide an algorithm to find a sub-optimal solution with any specified small tolerance from the globally optimal solution for the MPEP