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Article Dans Une Revue Mathematics of Control, Signals, and Systems Année : 2023

Stabilization of the complex double integrator by means of a saturated linear feedback

Yacine Chitour

Résumé

Consider the saturated complex double integrator, i.e., the linear control system $\dot x=Ax+B\sigma(u)$, where $x\in\R^4$, $u\in\R$, $B\in\R^4$, the $4\times 4$ matrix $A$ is not diagolizable and admits a non zero purely imaginary eigenvalue of multiplicity two, the pair $(A,B)$ is controllable and $\sigma:\R\to\R$ is a saturation function. We prove that there exists a linear feedback $u=K^Tx$ such that the resulting closed loop system given by $\dot x=Ax+B\sigma(K^Tx)$ is globally asymptotically stable with respect to the origin.
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Dates et versions

hal-04324645 , version 1 (05-12-2023)

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Yacine Chitour. Stabilization of the complex double integrator by means of a saturated linear feedback. Mathematics of Control, Signals, and Systems, 2023, 35 (2), pp.327-350. ⟨10.1007/s00498-022-00339-w⟩. ⟨hal-04324645⟩
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