Guaranteed Tracking Behavior in the Sense of Input-Output Spheres for Systems With Uncertain Parameters

A class of dynamical systems containing uncertain elements and subject to uncertain inputs is considered. The plant parameter uncertainties are assumed to be “unknown-but-bounded.” Design criteria are given for the synthesis of controllers for such systems, which guarantee that every input within a certain neighborhood of a nominal input gives rise to a corresponding output or system response in a prespecified neighborhood of a nominal output. These tracking specifications are formulated in terms of topological neighborhoods in normed function spaces, and feedback controllers are constructed by nonlinear state observers related to the uncertain plants and utilizing the measured output. These results, based primarily on fixed-point and operator norm techniques, provide quantitative servo designs and precise error bounds for the specified tracking behavior. The applicability of such derived criteria are demonstrated through synthesized controllers for two examples: a vibration isolation problem and a speed controller.