Simple recursive processes for determining Laplace and Z transforms of the zero-input responses of linear time-invariant systems

Author

O´Connell, Robert M.

Author_Institution

Electr. Eng. Dept., Missouri Univ., Columbia, MO, USA

Volume

45

Issue

2

fYear

2002

fDate

5/1/2002 12:00:00 AM

Firstpage

168

Lastpage

170

Abstract

Simple recursive methods are derived for quickly and easily writing either the Laplace transform of the zero-input response of a linear time-invariant continuous-time system or the z-transform of the zero-input response of a linear time-invariant discrete-time system. Application of the results to example systems shows that the derived processes make it possible to express the transform of the zero-input response nearly as easily as writing the transform of the zero-state response

Keywords

Laplace transforms; Z transforms; continuous time systems; control system analysis; discrete time systems; linear systems; Laplace transform; Z transform; control simulation; linear time-invariant continuous-time system; linear time-invariant discrete-time system; recursive methods; zero-input response; zero-state response; Delay effects; Difference equations; Differential equations; Discrete transforms; Inspection; Laplace equations; Linear systems; Time domain analysis; Transfer functions; Writing;

fLanguage

English

Journal_Title

Education, IEEE Transactions on

Publisher

ieee

ISSN

0018-9359

Type

jour

DOI

10.1109/TE.2002.1013882

Filename

1013882