CONVOLUTION Z-TRANSFORM METHOD APPLIED TO CERTAIN NONLINEAR DISCRETE SYSTEMS

摘要

In this paper the convolution z-transform method is applied to obtain an explicit solution of certain nonlinear difference equations. The explicit solution is often desired for system design as well as for obtaining the response for large intervals of time. In these difference equations which describe the physical discrete systems, it is assumed that the nonlinearities are "small. " This is necessitated by the form of solution applicable to the use of the convolution method. The advantage of the method is to systematize the procedure for the so¬lution as well as to obtain results in a closed form. The convergence of the solution is discussed as well as applications to certain examples.nThe examples chosen are feedback sampled-data systems with nonlinearities in the forward and feedback paths, respectively. Explicit solution in a closed form is obtained for the error as well as the output response. These results compare favorably with the nu¬merical solution of the nonlinear difference as a recurrence relationship.