Time-varying exponential stabilization of nonholonomic systems in power form

Systems in canonical power form have recently been used to model the kinematic equations of nonholonomic mechanical systems. McCloskey and Murray have had the idea of using the properties of homogeneous systems to derive exponentially stabilizing continuous time-periodic feedbacks for this class of systems. Motivated by this work, the present study extends a control design method previously proposed by Samson to the design of such homogeneous feedbacks. The approach here followed has the advantage of yielding simple and direct stability proofs. Homogeneity-related results needed for time-varying exponential stabilization are also provided.

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