Convolution z-transform method applied to certain nonlinear discrete systems

Abstract

This paper extends to discrete systems the method of complex convolution developed by Weber [6] for continuous systems. In this paper the convolutionz-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 solution as well as to obtain results in a closed form. The convergence of the solution is discussed as well as applications to certain examples. Two numerical examples are worked out to illustrate the method. Explicit approximate solution is obtained and the results compare favorably with the numerical solution of the nonlinear difference equation as a recurrence relationship.