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State-space solutions to standard H/sub 2/ and H/sub infinity / control problems

Doyle, J.C., Glover, K., Khargonekar, P.P., Francis, B.A.·1989·IEEE Transactions on Automatic Control
DOI 10.1109/9.29425
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Abstract

Simple state-space formulas are derived for all controllers solving the following standard H/sub infinity / problem: For a given number gamma >0, find all controllers such that the H/sub infinity / norm of the closed-loop transfer function is (strictly) less than gamma . It is known that a controller exists if and only if the unique stabilizing solutions to two algebraic Riccati equations are positive definite and the spectral radius of their product is less than gamma /sup 2/. Under these conditions, a parameterization of all controllers solving the problem is given as a linear fractional transformation (LFT) on a contractive, stable, free parameter. The state dimension of the coefficient matrix for the LFT, constructed using the two Riccati solutions, equals that of the plant and has a separation structure reminiscent of classical LQG (i.e. H/sub 2/) theory. This paper is intended to be of tutorial value, so a standard H/sub 2/ solution is developed in parallel.>

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Research works printed but not linked: 39

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Metadata

Authors
Doyle, J. C., Glover, K., Khargonekar, P. P., & Francis, B. A.
Venue
IEEE Transactions on Automatic Control
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Published
1989
Volume
34
Issue
8
Pages
831-847
ISSN
0018-9286 (ISSN-L)
DOI
10.1109/9.29425
OpenAlex
W2042106612
Cited by
5,569
References
0
FWCI
262.34
Type
journal article
Language
en
Open access
closed
Licence
ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html (vor)

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Doyle, J. C., Glover, K., Khargonekar, P. P., & Francis, B. A. (1989). State-space solutions to standard H/sub 2/ and H/sub infinity / control problems. IEEE Transactions on Automatic Control. https://doi.org/10.1109/9.29425

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