Robust feedback design: a time-domain fixed-point approach in L∞

Current interest in robust feedback design stems in part from the need for more precise and reliable tracking performance, namely, system behavior in which tracking errors, despite plant uncertainties and input disturbances, satisfy specified amplitude constraints in the time domain. Such performance, however, proves difficult to guarantee by means of transform constraints in the frequency domain. In LQ, H₂ and H_∞ designs, for example, transform constraints relate not to the amplitude of the tracking error but to the energy, i.e. not to the L_∞ norm of the error but to the L₂ norm [1]. Consequently, these methods are rather poor with respect to tracking performance [2,3]. In Horowitz´s QFT designs, transform constraints relate explicitly but heuristically to the amplitude C4]. Consequently, his methods are significantly better but are unfortunately system specific, highly graphic, and partially empiric [3,5]. To circumvent some of the major disadvantages of all these methods, we consider in this paper an alternative approach to QFT, one that provides both a precise, amplitude-oriented design formulation and a general, computeroriented design procedure.