On approximation structures for nonlinear systems

It is known that structures consisting of a finite number of linear dynamic systems followed by a memoryless nonlinear system are capable of uniformly approximating the output of a broad class of dynamic nonlinear systems arbitrarily well, over a large class of input signals. Past proofs for continuous-time systems are not constructive. In this dissertation, we show the existence of a constructive procedure for achieving such approximations for this class of systems. We give construction results for discrete-time systems as well. Also, for the first time, we give specific classes of input signals that satisfy the hypotheses of one of the more powerful prior approximation theorems. It is also shown that the members of a certain important family of feedback systems satisfy the conditions of this theorem.