Upper and lower bounds of the frequency response gain of sampled-data systems

This paper is concerned with the computations of the frequency response gain of sampled-data systems. The exact computations is intrinsically quite burdensome even at a fixed frequency, due to the infinite-dimensional nature involved in this problem. To facilitate an approximate computation instead, this paper gives three independent methods to compute upper and lower bounds of the frequency response gain. The first one is such that there is no parameter through which we can balance accuracy and the computational load, while the second and third are with such a parameter. In spite of this, the first methods will be found, in our numerical studies, to give quite a nice approximations in a reasonably short computations time, compared with other methods given in this paper and those available in the literature. It is also shown that our first methods has very close relationship to the sampled-data H2 and H∞ problems.