Feedback control of nonlinear systems

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Abstract
This paper deals with the design of (memoryless) state‐feedback laws for systems modelled by nonlinear differential equations which are affine in the inputs. The purpose of the design is to obtain a (locally) internally stable closed‐loop system in which the effect of exogenous inputs on a prescribed error (or, more in general, on a penalty variable) is attenuated. Two standard setups are considered: in the first one, the ratio between the energy associated with the penalty variable and that associated with the exogenous input is required to be bounded by a constant 0 < γ this setup includes (to some extent) the standardH∞control problemof linear system theory. In the second one, the penalty variable is required to converge to 0 ast∞; this setup generalizes the so‐calledservomechanism problemof linear system theory.

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