A fast algorithm to compute the controllability, decentralized fixed-mode, and minimum-phase radius of LTI systems

In this paper, an efficient algorithm is presented for solving the 2-D optimization problem which is associated with computing the robustness measures of a number of linear time-invariant (LTI) system properties such as the controllability radius, the decentralized fixed-mode radius, and the minimum-phase radius. Unlike methods such as gradient search methods, the proposed algorithm works well independent of the initial trial point, and obtains the minimum with a high level of confidence that it is indeed global. A numerical example is included.