Smooth weight optimization in ℋ∞ loop-shaping design

M. Osinuga, S. Patra, A. Lanzon

    Research output: Contribution to journalArticlepeer-review


    Smooth variation in the magnitude response of weights facilitates ℋ∞ loop-shaping design, as it prevents the cancellation of important modes of the system, for example, lightly damped poles/zeros of flexible structures, when the shaped plant is formed based on closed-loop design specifications. For accurate fitting of transfer functions to magnitude data, smooth weights also allow low-order transfer functions to be used when such smooth variations in their magnitude responses are computed point-wise in frequency. In this paper, smoothness constraints for weights, expressed as gradient constraints on a log scale in dB/decade, which is intuitive from a design perspective, are imposed in a weight optimization framework for ℋ∞ loop-shaping control. This work builds on [A. Lanzon, Weight optimization in ℋ∞ loop-shaping, Automatica 41 (1) (2005) 12011208], where additional constraints are formulated in linear matrix inequality (LMI) form to cast a complete weight optimization framework. The resulting algorithm thus maximizes the robust stability margin and simultaneously synthesizes smooth weights along with a stabilizing controller. A numerical example is given to elucidate the efficacy of the smoothness constraints in ℋ∞ loop-shaping control. © 2010 Elsevier B.V. All rights reserved.
    Original languageEnglish
    Pages (from-to)663-670
    Number of pages7
    JournalSystems and Control Letters
    Issue number11
    Publication statusPublished - Nov 2010


    • ℋ∞ loop-shaping
    • Robust control
    • Smoothness constraint
    • Weight optimization


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