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Generalized H2/H Control

  • Mario A. Rotea
  • Pramod P. Khargonekar
Conference paper
Part of the The IMA Volumes in Mathematics and its Applications book series (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.

Key words

H2 and H controller design state-space methods convex programming 

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Copyright information

© Springer-Verlag New York, Inc. 1995

Authors and Affiliations

  • Mario A. Rotea
    • 1
  • Pramod P. Khargonekar
    • 2
  1. 1.School of Aeronautics and AstronauticsPurdue UniversityWest LafayetteUSA
  2. 2.Department of Electrical Engineering and Computer ScienceThe University of MichiganAnn ArborUSA

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