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# Control of Nonlinear Chained Systems. From the Routh-Hurwitz Stability Criterion to Time-Varying Exponential Stabilizers

1 ICARE - Instrumentation, control and architecture of advanced robots
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : We show how any linear feedback law which asymptotically stabilizes the origin of a linear integrator system of order $(n-1)$ induces a simple continuous time-varying feedback law which exponentially stabilizes the origin of a nonlinear $(2,n)$ single-chain system. The proposed control design method is related to, and extends in the specific case of chained systems, a recent method developed by M'Closkey and Murray \cite{MC.MU3} for driftless systems in order to transform smooth feedback stabilizers yielding slow polynomial convergence into continuous homogeneous ones which ensure faster exponential convergence.
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https://hal.inria.fr/inria-00073563
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Submitted on : Wednesday, May 24, 2006 - 1:11:51 PM
Last modification on : Friday, February 4, 2022 - 3:21:41 AM
Long-term archiving on: : Sunday, April 4, 2010 - 9:22:29 PM

### Identifiers

• HAL Id : inria-00073563, version 1

### Citation

Pascal Morin, Claude Samson. Control of Nonlinear Chained Systems. From the Routh-Hurwitz Stability Criterion to Time-Varying Exponential Stabilizers. RR-3126, INRIA. 1997. ⟨inria-00073563⟩

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