SUFFICIENT CONDITIONS FOR THE FUNCTIONAL REPRODUCIBILITY OF TIME-VARYING, INPUT-OUTPUT SYSTEMS

The functional reproducibility of an input-output system refers to the capability of realizing a given class of functions as outputs of the system by the choice of appropriate inputs and initial conditions. For linear, time-varying, input-output systems we derive rank conditions that are sufficicent for the generations of all Ck outputs by means of C0 inputs. These rank conditions provide an alternative to the structure algorithm of L.M. Silverman and, in the linear, time-invariant case, reduce to a rank condition of M.K. Sain and J.L. Massey. We also give sufficient conditions for the local functional reproducibility of nonlinear, time-varying, input-output systems.