On the Complete "Discretization" of an nth -Order Linear Differential Equation Model to Obtain the Exact nth-Order Difference Equation Model with Correct "Initial-Sequence Values"

C.D. Johnson

Mathematical and Computer Modelling of Dynamical Systems, 1999, vol. 5, issue 1, 74-84

Abstract: The conversion of a given n th -order ordinary differential-equation model, with a stepwise-constant input, to an "equivalent" n th -order difference -equation model is an important procedure in many engineering applications, particularly in discrete-time/digital control theory for linear dynamical systems. That procedure, called "discretization", is not complete unless the given initial-conditions of the differential-equation model are properly incorporated into the corresponding "initial-sequence values" associated with the difference-equation model. The literature of discrete-time/digital control theory appears to be consistently incomplete in this latter regard. In this paper we derive the complete and exact discretization of an arbitrary n th -order linear, constant-coefficient, non-homogeneous ordinary differential equation model, with arbitrary initial-conditions and a stepwise-constant input, to obtain the corresponding exact equivalent n th -order, linear, constant-coefficient, non- difference equation model with correct initial-sequence values.

Date: 1999
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DOI: 10.1076/mcmd.5.1.74.3622

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