Abstract
Tracking and regulation refers to the ability of a control system to track/reject a given family of reference/disturbance signals modelled as solutions of a differential/difference equation. The problem can be posed as a stabilization problem with a constraint on the steady-state response of the system. For linear, time-invariant, systems the problem can be solved provided a system of linear matrix equations admits a solution. Properties of this system of equations are discussed, together with a general property of all controllers achieving tracking and regulation: the so-called internal model principle.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
(S) stands for stability and (R) for regulation.
Bibliography
Davison EJ (1976) The robust control of a servomechanism problem for linear time invariant multivariable systems. IEEE Trans Autom Control 21: 25–34
Francis BA, Wonham WM (1975) The internal model principle for linear multivariable regulators. Appl Math Optim 2:170–194
Wonham WM (1985) Linear multivariable control: a geometric approach, 3rd edn. Springer, New York
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this entry
Cite this entry
Astolfi, A. (2021). Tracking and Regulation in Linear Systems. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, Cham. https://doi.org/10.1007/978-3-030-44184-5_198
Download citation
DOI: https://doi.org/10.1007/978-3-030-44184-5_198
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-44183-8
Online ISBN: 978-3-030-44184-5
eBook Packages: Intelligent Technologies and RoboticsReference Module Computer Science and Engineering