RELATING H2 AND H-INFINITY BOUNDS FOR FINITE-DIMENSIONAL SYSTEMS

For a linear time invariant system, the infinity-norm of the transfer function can be used as a measure of the gain of the system. This notion of system gain is ideally suited to the frequency domain design techniques such as H-infinity optimal control. Another measure of the gain of a system is the H-2 norm, which is often associated with the LQG optimal control problem. The only known connection between these two norms is that, for discrete time transfer functions, the H-2 norm is bounded by the H-infinity norm. It is shown in this paper that, given precise or certain partial knowledge of the poles of the transfer function, it is possible to obtain an upper bound of the H-infinity norm as a function of the H-2 norm, both in the continuous and discrete time cases. It is also shown that, in continuous time, the H-2 norm can be bounded by a function of the H-infinity norm and the bandwidth of the system.