J-inner-outer factorization, J-spectral factorization, and robust control for nonlinear systems

J.A. Ball, A.J. van der Schaft

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    Abstract

    The problem of expressing a given nonlinear state-space system as the cascade connection of a lossless system and a stable, minimum-phase system (inner-outer factorization) is solved for the case of a stable system having state-space equations affine in the inputs. The solution is given in terms of the stabilizing solution of a certain Hamilton-Jacobi equation. The stable, minimum-phase factor is obtained as the solution of an associated nonlinear spectral factorization problem. As an application, one can arrive at the solution of the nonlinear H/sub /spl infin//-control problem for the disturbance feedforward case.
    Original languageEnglish
    Pages (from-to)379-392
    JournalIEEE transactions on automatic control
    Volume41
    Issue number3
    DOIs
    Publication statusPublished - 1994

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