Abstract
The paper presents the first result on nonholonomic systems enjoying input to state stability (ISS) properties. Although it is known that smooth stabilizability implies ISS, the converse is not generally true. This leaves the possibility of non-smoothly stabilizable systems being ISS with respect to a particular input, after an appropriate feedback transformation. This is shown to be true for the case of the unicycle with a dynamic extension, in a particular topology induced by a metric appropriate for this type of systems. A feedback control law renders the closed-loop system locally ISS in the particular topology. Potential applications include stability and robustness analysis of formations of mobile robots.
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