Converting Smooth, Time-Varying, Asymptotic Stabilizers for Driftless Systems to Homogeneous, Exponential Stabilizers

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Richard M. Murray and Robert T. M'Closkey
1995 European Control Conference (Rome)

The main result of this paper is a theorem that allows smooth, time-varying controllers which asymptotically stabilize a driftless nonlinear system to be converted to homogeneous, time-varying controllers which provide {\em exponential} stability. The resulting controllers are smooth everywhere except the origin and are easily computed given the original asymptotic stabilizer. We illustrate the result with experimental results on a simple mobile robot.