MINIMIZATION OF A CLOSED-LOOP RESPONSE TO A FIXED INPUT FOR SISO SYSTEMS

It is shown that the problem of minimizing a regulated response of a s ingle-input/single-output system due to a fixed bounded input can be c onverted, via polynomial techniques, to a linear infinite-dimensional Chebyshev data fitting problem. Approximating feasible solutions withi n any specified degree of accuracy can be obtained by converting the o riginal problem into a sequence of increasingly large, finite-dimensio nal Chebyshev approximation problems, for which solution stable and ef ficient numerical methods exist. A direct formula for calculating tigh t upper-bounds to the approximation error is provided. The link betwee n the present algebraic approach and the Dahleh and Pearson functional analytic one is also discussed.