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A theoretical framework for gain scheduling

The weighted incremental norm approach was originally introduced as a natural framework for extending well‐known H∞ linear control concepts into the nonlinear context. In this paper, we investigate the numerous links between this new approach and the classical gain‐scheduling technique. Although based on heuristic rules, gain‐scheduled control is probably the most widespread nonlinear technique. In this paper, we point out that the control objectives of the gain‐scheduled controller design can be expressed as the weighted incremental norm minimization of a nonlinear operator. The result interest is twofold: it first provides a rigorous mathematical formulation of the gain‐scheduling problem. Furthermore, existing gain‐scheduling techniques can be interpreted as approximate solutions to the weighted incremental norm minimization of a nonlinear operator. Copyright © 2003 John Wiley & Sons, Ltd.