Minimization of a regulated response to a fixed input

The problem of minimizing a regulated output due to a specific bounded input is solved in the SISO (single-input single-output) discrete-time case. It is shown that, in most situations, the optimal solution will not exist, but given any epsilon >0, it is possible to find a suboptimal solution with performance within epsilon of the optimal performance. The proposed approach is extended to the problem of shaping the error transient response. It is shown how time-domain templates can be used in this problem in the same way that frequency-weighting functions are used in the H/sup infinity / and H/sup 2/ problems.<>