Computation of the H∞ norm of a transfer function

A new method for computing G_∞, the H^∞ norm of a given transfer function G(s) is proposed. In this paper, we use the pole-zero diagram of G(s), the root locus concept, and the jω-axis transmission zeros of γ²I-G^T(-s)G(s) to quickly locate a narrow frequency interval which brackets the supremum of [G(jω)]. Then Brent´s method (an improved parabolic interpolation search method) is employed to find the maximum of [G(jω)] over the initial frequency bracket. The proposed approach is faster than the existing frequency search and ω bisection search methods since the initial frequency interval we obtain usually is quite small and the Brent´s method in general is much faster than the bisection method.