## A Bisection Method for Computing the H_infinity-Norm of a Transfer Matrix and Related ProblemsS. Boyd, V. Balakrishnan, and P. Kabamba
Inspired by recent work of Byers we establish a simple connection between the
singular values of a transfer matrix evaluated along the imaginary axis and the
imaginary eigenvalues of a related Hamiltonian matrix. We give a simple linear
algebraic proof of this connection, and also a more intuitive explanation based
on a certain indefinite quadratic optimal control problem and the work of
Willems. This result yields a simple bisection algorithm to compute the
H_infinity norm of a transfer matrix. The bisection method is far more
efficient than algorithms which involve a search over frequencies, and of
course the usual problems associated with such methods (such as determining how
fine the search should be) do not arise. The method is readily extended to
compute other quantities of system-theoretic interest, |