Discussion on the Determination Method of the Undetermined Coefficient in the Response Solution of Linear Time-Invariant Discrete System

Abstract

There are some problems in the existing methods for determining the undetermined coefficients in the linear time-invariant discrete system response solution, which are mainly to determine whether the conditions for the undetermined coefficients of the general solution of the classical solution can be extended, and the ambiguity of the conditions and the extension of the conditions for determining the undetermined coefficients of the general solution of the zero input response, and the error of using condition when determining the undetermined coefficient of general solution of zero state response. In this paper, by means of the mathematical analysis of the difference equation model of a linear time-invariant discrete system, firstly, based on the existing analytical methods, the conditional extension method for determining the undetermined coefficients of the classical solution is given, and the classical solution is analyzed under the extended conditions. Then, the method to determine the undetermined coefficient in the solution of zero input and zero state response is analyzed, and the unclear conditions and errors in the existing methods to determine the undetermined coefficient are corrected. Finally, by comparing the system response obtained by the classical method with the zero input method and the zero state method, the correctness and validity of the method proposed in this paper are verified, so that the premise error will not occur when the linear time-invariant system model is used for problem analysis in practical engineering.