## Exponential Stabilization of Driftless Nonlinear Control Systems (1995)

Citations: | 50 - 3 self |

### BibTeX

@MISC{M'Closkey95exponentialstabilization,

author = {Robert Thomas M'Closkey and III},

title = {Exponential Stabilization of Driftless Nonlinear Control Systems},

year = {1995}

}

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### Abstract

This dissertation lays the foundation for practical exponential stabilization of driftless control systems. Driftless systems have the form, x = X 1 (x)u 1 + \Delta \Delta \Delta + Xm (x)um ; x 2 R n : Such systems arise when modeling mechanical systems with nonholonomic constraints. In engineering applications it is often required to maintain the mechanical system around a desired configuration. This task is treated as a stabilization problem where the desired configuration is made an asymptotically stable equilibrium point. The control design is carried out on an approximate system. The approximation process yields a nilpotent set of input vector fields which, in a special coordinate system, are homogeneous with respect to a non-standard dilation. Even though the approximation can be given a coordinate-free interpretation, the homogeneous structure is useful to exploit: the feedbacks are required to be homogeneous functions and thus preserve the homogeneous structure in the close...