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State-space solutions to standard H2 and H∞ control problems

Doyle, John C. and Glover, Keith and Khargonekar, Pramod P. and Francis, Bruce A. (1989) State-space solutions to standard H2 and H∞ control problems. IEEE Transactions on Automatic Control, 34 (8). pp. 831-847. ISSN 0018-9286.

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Simple state-space formulas are derived for all controllers solving the following standard H∞ problem: For a given number γ>0, find all controllers such that the H∞ norm of the closed-loop transfer function is (strictly) less than γ. 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 γ2. 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. H2) theory. This paper is intended to be of tutorial value, so a standard H2 solution is developed in parallel.

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Doyle, John C.0000-0002-1828-2486
Additional Information:© 1988 IEEE. Manuscript received April 25, 1988; revised December 15, 1988. Paper recommended by Past Associate Editor at Large, G. Stein. This work was supported by the AFOSR, NASA, NSF, ONR, SERC, and NSERC. The authors wish to thank B. Morton, T. Sideris, R. Smith, M. Newlin, K. Zhou, B. Bodenheimer, G. Balass, P. Campo, B. Pearson, and A. Tannenbaum for helpful discussions.
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)UNSPECIFIED
Office of Naval Research (ONR)UNSPECIFIED
Science and Engineering Research Council (SERC)UNSPECIFIED
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Subject Keywords:optimal control; state-space methods; transfer functions
Issue or Number:8
Record Number:CaltechAUTHORS:DOYieeetac89
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3087
Deposited By: Archive Administrator
Deposited On:15 May 2006
Last Modified:02 Oct 2019 22:59

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