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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:
93D15Stabilization of systems by feedback
93C10Nonlinear control systems
93C15Control systems governed by ODE
34H05ODE in connection with control problems