On computing the L2 norm of a generalized discrete-time system

We give explicit analytic formulas for computing the L₂ norm of a discrete-time generalised system whose rational transfer matrix function may be improper or polynomial. The norm is expressed in terms of solutions of generalized Lyapunov equations, written down with coefficients from a special type of realisation of the underlying transfer function matrix, much in the same spirit of the standard (proper) case. The main result hints to a numerically-sound prototype algorithm that relies on standard reliable software for computing solutions of generalised Lyapunov equations.