A geometric series approach to modelling discrete-time state equations from continuous-time state equations

Abstract

A geometric series approach for approximating the state transition matrix of u continuous-time state equation by a discrete-time state transition matrix is developed in this paper. A discrete-time state equation is constructed for approximation of the continuous-time state equation. The discrete-time state transition matrix is modified to derive a generalized approximate numerical differentiator. Also, it is shown that several commonly used conversion procedures are special cases of this method.