Communications in Information and Systems

Volume 8 (2008)

Number 1

An expanded method to robustly stabilize uncertain nonlinear systems

Pages: 55 – 70

DOI: http://dx.doi.org/10.4310/CIS.2008.v8.n1.a4

Authors

Jason Polendo

Chunjiang Qian

Abstract

The current literature on the global state feedback stabilization of nonlinear systems modeled by a perturbed chain of nonlinear integrators, particularly those whose linearization about the origin may contain uncontrollable modes, essentially contains two methods: a smooth controller scheme (only under strict assumptions) and a non-smooth one. The most general of these systems could previously only be globally asymptotically stabilized by continuous time-invariant state feedback controller, where this paper shows that now at least C1 stabilization can be achieved, upon existence, in this more general setting. This new method can be seen as not only a natural unification of the smooth and nonsmooth methods, but also a generalization to construct smoother stabilizers.

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