On computing the L/sup 2/-induced norm of finite-horizon systems

Abstract

We present a bisection type algorithm for computing the L/sup 2/-induced norm of a linear time invariant system over a finite time horizon. The main difficulty in using bisection algorithms for finite horizon norm computation, namely the discreteness of the spectrum, is circumvented by using a winding number method. We derive an integral formula that counts the number of singular values of the finite horizon operator that are larger than a certain pre-specified level.