A bisection method for computing the H ∞ norm of a transfer matrix and related problems

摘要: We establish a correspondence between the singular values of transfer matrix evaluated along imaginary axis and eigenvalues related Hamiltonian matrix. give simple linear algebraic proof, also more intuitive explanation based on certain indefinite quadratic optimal control problem. This result yields bisection algorithm to compute H∞ norm The method is far efficient than algorithms which involve search over frequencies, usual problems associated with such methods (such as determining how fine should be) do not arise. readily extended other quantities system-theoretic interest, for instance, minimum dissipation A variation can be used solve Armijo line-search problem no computation required single norm.