Abstract
In this chapter we consider the H 2 optimal control problem. Given a controlled linear system with a white noise disturbance input, we show that the size (in an appropriate sense) of the controlled output is equal to the H 2 norm of the closed loop transfer matrix. Motivated by this, we define the performance of the controlled system to be the H 2 norm of the closed loop transfer matrix. This gives rise to the H 2 optimal control problem: for a given control system, minimize the square of the H 2 norm of the closed loop transfer matrix over the class of all internally stabilizing feedback controllers.
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
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag London
About this chapter
Cite this chapter
Trentelman, H.L., Stoorvogel, A.A., Hautus, M. (2001). The H 2 optimal control problem. In: Control Theory for Linear Systems. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-0339-4_11
Download citation
DOI: https://doi.org/10.1007/978-1-4471-0339-4_11
Publisher Name: Springer, London
Print ISBN: 978-1-4471-1073-6
Online ISBN: 978-1-4471-0339-4
eBook Packages: Springer Book Archive