State-space solution to weight optimization problem in ℋ ∞ loop-shaping control

M. Osinuga, S. Patra, A. Lanzon

    Research output: Contribution to journalArticlepeer-review


    This paper proposes a state-space solution to weight optimization problem in ℋ ∞ loop-shaping control. A pointwise-in-frequency weight optimization framework is transformed into convex optimization searches that are independent of frequency. The introduced optimization problem therefore avoids gridding of the frequency space and consequently, the inaccuracies attributed to fitting transfer functions to magnitude data. In this optimization problem, the order of the weight is specified 'a priori', thus facilitating the synthesis of low-order controllers, which is desirable from an implementation perspective. The proposed solution algorithm simultaneously synthesizes a robust stabilizing controller and a loop-shaping weight (pre-compensator) that maximize the robust stability margin subject to constraints on the performance and the singular values of the weight. Three numerical examples are given to illustrate the effectiveness of the technique. © 2012 Elsevier Ltd. All rights reserved.
    Original languageEnglish
    Pages (from-to)505-513
    Number of pages8
    Issue number3
    Publication statusPublished - Mar 2012


    • ℋ ∞ loop-shaping
    • Convex optimization
    • Robust stability margin
    • Weight optimization


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