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Generalized H 2/H ∞ Control

  • Conference paper
Robust Control Theory

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 66))

Abstract

In this paper we consider the problem of finding a controller that minimizes an upper bound on the worst case overshoot of a controlled output in response to arbitrary but bounded energy exogenous inputs subject to an inequality constraint on the H ∞ norm of another closed loop transfer function. This problem, which we define as the generalized H 2/H ∞ control problem, can be interpreted and motivated as a problem of optimal nominal performance subject to a robust stability constraint. We consider both state-feedback and output feedback problems. It is shown that in the state-feedback case one can come arbitrarily close to the optimal performance measure using memory-less state-feedback. Moreover, the state-feedback generalized H 2/H ∞ problem can be converted into a convex optimization problem over a set of matrices defined in terms of affine matrix inequalities. For output feedback problems, we show that the generalized H 2/H ∞ control problem is equivalent to a state-feedback generalized H 2/H ∞ control problem of a suitably constructed auxiliary plant. An output feedback controller that solves the generalized H 2/H ∞ synthesis problem may be readily constructed from the solution to the auxiliary state-feedback problem and the solution to the standard H ∞ filtering algebraic Riccati equation. The structure of this controller is similar to that of the so-called central H ∞ controller.

School of Aeronautics and Astronautics, Purdue University, West Lafayette, Indiana 47907. The work of the first author was supported by National Science Foundation under RIA no. ECS-91-08493.

Department of Electrical Engineering and Computer Science, The University of Michigan, Ann Arbor, Michigan 48109. The work of the second author was supported by National Science Foundation under grants no. ECS-90-01371, Airforce Office of Scientific Research under contract no. AFOSR-90-0053, Army Research Office under grant no. DAAH04-93-G-0012.

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Author information

Authors and Affiliations

  1. School of Aeronautics and Astronautics, Purdue University, West Lafayette, Indiana, 47907, USA

    Mario A. Rotea

  2. Department of Electrical Engineering and Computer Science, The University of Michigan, Ann Arbor, Michigan, 48109, USA

    Pramod P. Khargonekar

Authors
  1. Mario A. Rotea
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  2. Pramod P. Khargonekar
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Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Toronto, M5S 1A4, Toronto, Ontario, Canada

    Bruce A. Francis

  2. Department of Electrical Engineering and Computer Science, University of Michigan, 48109, Ann Arbor, MI, USA

    Pramod P. Khargonekar

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© 1995 Springer-Verlag New York, Inc.

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Rotea, M.A., Khargonekar, P.P. (1995). Generalized H 2/H ∞ Control. In: Francis, B.A., Khargonekar, P.P. (eds) Robust Control Theory. The IMA Volumes in Mathematics and its Applications, vol 66. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8451-9_5

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  • DOI: https://doi.org/10.1007/978-1-4613-8451-9_5

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-8453-3

  • Online ISBN: 978-1-4613-8451-9

  • eBook Packages: Springer Book Archive

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