Abstract :
Consider the finite subset {(xi, yi)} of input-output pairs. A common design objective is to specify a system, S, such that yi = Sxi holds on the set in question. Moreover, S should also be well behaved on a larger input space. In a recent study [1], the author solved a synthesis problem of the above type. In that study the input and output spaces are taken to be arbitrary Hilbert Resolution spaces. At present we focus attention also on the Hilbert space L2(v). It is shown that the operator theoretic solution of [1] can be realized by a differential equation set of the form. z(t) = A(t)z(t) + b(t)x(t) y(t) = c(t)z(t), t ?? v where {A,b,c} are explicitly specified from the input-output data.
