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Global stabilization and restricted tracking for multiple integrators with bounded controls. (English) Zbl 0752.93053

Summary: Necessary and sufficient conditions for globally stabilizing linear systems with bounded controls are known. However, it has been shown by H. J. Sussmann and Y. Yang [Technical Report SYCON-91-01, Rutgers center for systems and control, New Brunswick, NJ (1991)] that, for single-input systems, no saturation a linear feedback can globally stabilize a chain of integrators of order \(n\), with \(n\geq 3\). We propose a nonlinear combination of saturation functions of linear feedbacks that globally stabilizes a chain of integrators of arbitrary order. The appealing feature of the proposed control is that it is fairly easy to construct. It is linear near the origin and can also be used to achieve trajectory tracking for a class of trajectories restricted by the absolute on the input.

MSC:

93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93B05 Controllability
93C05 Linear systems in control theory
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References:

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