Robust stabilization of input/output linearizable systems under uncertainty and disturbances

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Abstract
In recent years, differential geometric techniques have been used to transform nonlinear systems into linear systems. Once such equivalent linear systems are obtained, classical linear controllers are designed to achieve desired stability and performance properties. A major critism against these techniques is their lack of guarantee for robustness. In particular, the design of controllers for transformed nonlinear systems under the influence of both disturbances and (parametric) modeling errors is not well‐known. This article presents a methodology to design robust stabilizing controllers for such uncertain and perturbed nonlinear systems.For feedback linearizable systems, the method guarantees that the nonlinear system has nominally linear input/output dynamics and is stable for the given class of bounded parametric uncertainty and disturbances. The new concepts and the proposed design procedure are shown for an isothermal reactor with second‐order kinetics.

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