Time-domain QFT based on fixed points and homotopic invariance in L∞

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Abstract
The quantitative feedback theory (QFT) developed by I. M. Horowitz is of recent widespread interest. An extension of traditional feedback principles, QFT provides design methods in the frequency domain yielding prescribed hard constraints on the amplitudes of tracking errors in the time domain. These methods prove significantly more effective than those of the more modern LQ, H2, and H∞ theories. Inherent in QFT, however, are several adverse features, in particular, a frequency and time relationship that is partially heuristic, a design process that is highly graphic, and a treatment of SISO, MIMO, linear, and non-linear systems that is somewhat case-dependent. An alternative QFT circumventing these features is the focus of this paper. An alternative deriving from a general formulation in the time domain alone, providing a unified set of amplitude- and computer-oriented design criteria, and yielding prescribed, fully analytic constraints on tracking errors is considered. Specifically, we formulate system stability, design criteria, and tracking constraints in terms of fixed-point conditions in a combined time-domain and L∞ setting. These conditions are established by the techniques of homotopic invariance and tailored to the tracking dynamics of feedback systems.