On computing the infinity norm

An iterative algorithm is given for computing the infinity norm of the transfer matrix of a bounded, linear, time-invariant, finite-dimensional system. The procedure, which is based on the numerically stable QZ algorithm, enables the infinite norm to be computed with a guaranteed accuracy. No ad hoc procedures, such as those for selecting a suitable grid of frequencies, for example, are used. The degree of accuracy is under the direct control of the user, with each additional decimal place of accuracy requiring ≈3.3 calls to the QZ algorithm. Experience has shown the algorithm to function reliably and in reasonable time for models of order as large as 56