A new bound of the /spl Lscr//sub 2/[0, T]-induced norm and applications to model reduction

We present a simple bound on the finite horizon /spl Lscr//sub 2/[0, T]-induced norm of a linear time-invariant (LTI), not necessarily stable system which can be efficiently computed by calculating the /spl Hscr//sub /spl infin// norm of a shifted version of the original operator. As an application, we show how to use this bound to perform model reduction of unstable systems over a finite horizon. The technique is illustrated with a non-trivial physical example relevant to the appearance of time-irreversible phenomena in statistical physics.