Uncertain systems: Robustness of ultimate boundedness control with respect to neglected dynamics

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Uncertain systems: Robustness of ultimate boundedness control with respect to neglected dynamics

Leitmann, G. / Ryan, E. P. / Steinberg, A.

Abstract Feedback control of a class of imperfectly known dynamical systems is considered. On the basis of known functional properties and bounds relating to the uncertain elements of the generic system and initially neglecting actuator and sensor dynamics, a feedback structure is first determined (using established Lyapunov-based techniques [1],[2]) which guarantees uniform ultimate boundedness of all motions of the reduced-order system (i.e. the uncertain system in the absence of actuator and sensor dynamics). Robustness properties of the full system are subsequently derived (related questions of robustness are also addressed in e.g., [3]-[6]). In particular, it is shown that the feedback controlled system is structurally stable in the sense that the features designed for the reduced-order system are qualitatively retained in the presence of sufficiently fast actuator or sensor dynamics. Moreover, explicit threshold measures of "fastness" of these dynamics are obtainable.