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 noti on of system gain is ideally suited to the frequency domain design tec hniques such as H-infinity optimal control. Another measure of the gai n 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 n orms is that, for discrete time transfer functions, the H-2 norm is bo unded by the H-infinity norm. It is shown in this paper that, given pr ecise or certain partial knowledge of the poles of the transfer functi on, 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 c ases. It is also shown that, in continuous time, the H-2 norm can be b ounded by a function of the H-infinity norm and the bandwidth of the s ystem.