On Initial Conditions for State-space Discrete-time Models

Shin Kawai and Noriyuki Hori

Keywords

Initial Condition, StateSpace Form, Exact DiscreteTime Model, Mapping DiscreteTime Models

Abstract

An assumption on state-space discrete-time models of a linear time-invariant continuous-time system that was imposed in our previous studies, has been removed to accommodate an arbitrary initial condition. A sufficient condition on the initial value of the state vector is presented to ensure that the output response of a discrete-time model starts from the same value as the continuous-time original. As important examples, formulae are derived for the initial states of the exact and the mapping discrete-time models. Typical simulation results are also presented to illustrate the importance of the choice of the initial values, especially for the mapping model.

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