LFTB: An optimized algorithm to bound worst-case frequency response functions

Presents an optimized algorithm to calculate a bound on the largest frequency response function that results when n parameters may vary simultaneously. The bound is obtained as the solution to a convex optimization problem known as semidefinite programming problem. The proposed algorithm is based on a known interior-point method for solving semidefinite programs. Proper utilization of the structure, of the specific semidefinite program, leads to an algorithm whose cost grows as O(n³) flops per iteration. Available general-purpose algorithms, do not utilize the specific problem structure, and their cost grows as O(n⁴) flops per iteration. Thus, the optimized algorithm in the paper achieves a cost reduction proportional to n, which is substantial for problems with hundreds of parameters. Additional savings are obtained when the frequency response function under study comes from a system with nominal circular symmetry