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Exponential stabilization of non-holonomic systems: an ENI approach. (English) Zbl 1017.93021

The non-holonomic system \[ \dot y_{i} = u_{i},\quad i=1,2, \qquad \dot y_{3} = k_{2}y_{2}u_{1} - k_{1}y_{1}u_{2}, \qquad \dot y_{j} = y_{j-1}u_{1}, \quad j=4,\ldots,n \] is shown to be equivalent via some smooth changes of coordinates to other forms of nonlinear systems. Consequently the feedback controllers obtained for the above systems are applicable to the equivalent ones.

MSC:

93B10 Canonical structure
93D15 Stabilization of systems by feedback
93B17 Transformations
70F25 Nonholonomic systems related to the dynamics of a system of particles
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