Matrix-based bounding vs. element-wise bounding for the MPEP global optimization

In this paper, we compare the matrix-based bounding and the element-wise bounding concerning the global optimization for the matrix product eigenvalues problem (MPEP), which addresses many typical bilinear matrix inequality problems for control synthesis. It is shown that using the matrix-based bounding has some advantages in the consideration of the global optimization for MPEP over the element-wise bounding. Numerical experiments illustrate that the algorithm using the matrix-based bounding is better than that of the element-wise bounding in the total computational time