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An expanded method to robustly stabilize uncertain nonlinear systems. (English) Zbl 1158.93394

Summary: 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 \(C^{1}\) 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.

MSC:

93D15 Stabilization of systems by feedback
93C15 Control/observation systems governed by ordinary differential equations
93C10 Nonlinear systems in control theory
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