  We consider the computation of H-infinity norms for
Single-Input-Single-Output (SISO) time-delay systems, which are described by
delay differential algebraic equations. Unlike the iterative level set methods
in the literature, we present a novel numerical method to compute the
H-infinity norm. This method requires solving one eigenvalue problem of at most
twice the size of the eigenvalue problem in every iteration of a level set
method, but in practice often considerably lower. We first show that the
computation of extrema of the transfer function can be turned into the
computation of the imaginary axis zeros of a transcendental function. We
compute these zeros by a predictor-corrector type algorithm. It is known that
the H-infinity norm of delay differential algebraic systems, which can model
both retarded and neutral type systems, might be sensitive with respect to
arbitrarily small delay perturbations. This recently led to the concept of
strong H-infinity norms, which explicitly take into account such small delay
perturbations. We present a direct numerical method to compute the strong
H-infinity norm of SISO time-delay systems. Our algorithm is applicable to the
closed-loop system of interconnections (series, parallel, feedback, junctions)
of time-delay systems and/or controllers.
