Abstract
The paper addresses the synthesis of a smooth dynamic feedback for a class of nonlinear (nonholonomic) systems. The proposed technique provides asymptotic stability and exponential convergence to a desired equilibrium manifold. The manifold is a function of the generalized co-ordinates. Application of the proposed technique to control of a class of nonholonomic systems is presented. We also show that some nonholonomic systems (e.g. Brockett's bilinear system) controlled by the proposed time-invariant dynamic feedback converge asymptotically to an arbitrary small ball centered at the origin of the state space under certain circumstances.
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