Abstract
This chapter constitutes a different development of Chap. 2. We consider the problem of representing the solutions of nonhomogeneous (i.e., with forcing term) systems of linear differential equations. We present the variation of constants formula and the method of undetermined coefficients. Moreover, we illustrate the qualitative notions of transient and steady state solution. Finally we present the Laplace transform method and, as an application, we discuss the frequency response analysis of a system under periodic input.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
According to a more correct terminology, a system of the form (4.1) should be called an “affine” system; however, the term “linear nonhomogeneous” is very frequent in the literature.
- 2.
- 3.
On the other hand, it is easy to check that there exists a constant or periodic solution only if the forcing term is, respectively, constant or periodic.
- 4.
Recall that \(p_i=0\) \((i=1,2)\) does not imply in general \(q_i=0\).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Bacciotti, A. (2019). Linear Systems with Forcing Term. In: Stability and Control of Linear Systems. Studies in Systems, Decision and Control, vol 185. Springer, Cham. https://doi.org/10.1007/978-3-030-02405-5_4
Download citation
DOI: https://doi.org/10.1007/978-3-030-02405-5_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-02404-8
Online ISBN: 978-3-030-02405-5
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)