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Global finite-time stabilisation by output feedback for a class of uncertain nonlinear systems. (English) Zbl 1210.93064

Summary: This article considers the problem of global finite-time stabilisation by output feedback for a class of nonlinear systems comprised of a chain of power integrators perturbed by an uncertain vector field. To solve the problem, we first construct a homogeneous observer and controller in a recursive way for the nominal system without the perturbing nonlinearities. Then, using the homogeneous domination approach, we scale the homogeneous observer and controller with an appropriate choice of gain to render the uncertain nonlinear system globally finite-time stable. Due to the use of a reduced-order observer, the proposed output feedback controller is applicable to those systems with unknown gains associated with the power integrators.

MSC:

93D15 Stabilization of systems by feedback
93C10 Nonlinear systems in control theory
93C15 Control/observation systems governed by ordinary differential equations
34H05 Control problems involving ordinary differential equations
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