Controllability to the origin implies state-feedback stabilizability for discrete-time nonlinear systems

Shigeru Hanba

doi:10.1016/j.automatica.2016.09.046

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arXiv · 1505.05937

Controllability to the origin implies state-feedback stabilizability for discrete-time nonlinear systems

Shigeru Hanba

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Abstract

The problem of state-feedback stabilizability of discrete-time nonlinear systems has been considered in this note. Two assertions have been proved. First, if the system is $N$-step controllable to the origin, then there is a state feedback control law for which the trajectory of the closed-loop system converges to the origin in $N$ steps. Second, if the system is asymptotically controllable to the origin and satisfies the controllability rank condition at the origin, then there is a state feedback control law for which the trajectory of the closed-loop system converges to the origin in finite steps.

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BibTeX RIS

Shigeru Hanba. 2018-04-18. Controllability to the origin implies state-feedback stabilizability for discrete-time nonlinear systems. https://doi.org/10.1016/j.automatica.2016.09.046

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