ALMOST DISTURBANCE DECOUPLING FOR NONLINEAR SYSTEMS VIA CONTINUOUS FEEDBACK

Abstract This paper addresses the problem of almost disturbance decoupling with internal stability (ADD) for inherently nonlinear systems with uncontrollable unstable linearization. Although achieving ADD in the sense of the L 2 –gain is usually impossible by smooth state feedback, we show that there exists a non-smooth but continuous state feedback control law, yielding a closed-loop system which is globally strongly stable in the absence of disturbance, and in the presence of disturbance, whose L 2 –gain between the disturbance input and the system output is less than or equal to an arbitrarily small number γ > 0. In contrast to the existing results in the literature, all the growth conditions imposed previously to achieve ADD via smooth state feedback are completely removed under this continuous feedback framework, enabling one to deal with a significantly larger class of nonlinear systems.

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