Feedback stabilization about attractors and the problem of asymptotic disturbance rejection

The authors present a solution to the problem of asymptotic disturbance rejection for a broad class of unstable nonlinear control systems. Containing asymptotic stabilization as a special case, this problem also entails ensuring that bounded disturbances produce bounded variations in the system state trajectories, a property not implied in general by asymptotic stability in the nonlinear case. In order to obtain the required version of BIBO (bounded input bounded output) stability, the authors extend some recent stabilization schemes to the setting of feedback stabilization about a compact attractor. In the asymptotic disturbance rejection problem they use the internal model principle to introduce a compact attractor (in an augmented zero dynamics) which is then stabilized, yielding both output regulation and bounded state trajectories