Abstract
This paper considers H∞-control under the assumption that all the states are available for feedback. It can be shown that in that case we can restrain ourselves to static feedback. This paper gives extensions and a more intuitive explanation of recent results. Under a number of assumptions necessary and sufficient conditions are given for the existence of a stabilizing feedback such that the closed loop system has H∞ norm less than or equal to some predetermined bound γ. It is shown that if these assumptions are not met then by disturbing the system in such a way that these assumptions are satisfied we can find results about the existence of these desired feedbacks in more general cases.
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.
References
J.C. Doyle, K. Glover, P.P. Khargonekar and B.A. Francis, State space solutions to standard H2 and H. control problems, American control conference, Atlanta, 1988.
P.P Khargonekar,I.R. Petersen and M.A. Rotea, H∞—optimal control with state feedback,To appear in IEEE Trans. Automat. Contr.,1988.
P.P Khargonekar,I.R. Petersen and K.Zhou, Robust stabilization and H ∞ control, Submitted for publication IEEE Trans. Aut. Contr.,September 1987.
I.R. Petersen, Disturbance attenuation and H∞ optimization: A design method based on the algebraic Riccati equation, IEEE Trans. Aut. Contr.,Vol AC-32,No. 5, May 1987,pp. 427–429.
A.A. Stoorvogel, The singular zero sum differential game with stability using H∞ control theory,Submitted for publication Math. Contr. Sign. Syst..
J.C. Willems,Least squares optimal control and the algebraic Riccati equation, IEEE Trans. Aut. Contr.,Vol 16, No. 6, December 1971, pp. 621–634.
K. Zhou and P.P. Khargonekar, An algebraic Riccati equation approach to H 00 optimization, Syst. Contr. Lett., Vol. 11, No. 2, August 1988, pp. 85–91.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Birkhäuser Boston
About this chapter
Cite this chapter
Stoorvogel, A.A. (1990). H∞ Control with State Feedback. In: Kaashoek, M.A., van Schuppen, J.H., Ran, A.C.M. (eds) Robust Control of Linear Systems and Nonlinear Control. Progress in Systems and Control Theory, vol 4. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4484-4_33
Download citation
DOI: https://doi.org/10.1007/978-1-4612-4484-4_33
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-8839-8
Online ISBN: 978-1-4612-4484-4
eBook Packages: Springer Book Archive