TY - GEN

T1 - On the stabilizability of multiple integrators by means of bounded feedback controls

AU - Sussmann, Hector J.

AU - Yang, Yudi

PY - 1992/1/1

Y1 - 1992/1/1

N2 - It is known that a linear x= Ax + Bu can be stabilized by means of a smooth bounded control if and only if it has no eigenvalues with positive real part, and all the uncontrollable modes have a negative real part. Here, the authors investigate, for single-input systems, the question of whether such systems can be stabilized by means of a feedback u = σ(h(x)), where h is linear and σ(s) is a saturation function such as sign(s) min(|s|,1). A stabilizing feedback of this particular form exists if A has no multiple eigenvalues, and also in some other special cases such as the double integrator. It is shown that for the multiple integrator of order n, with n ≥ 3, no saturation of a linear feedback can be globally stabilizing.

AB - It is known that a linear x= Ax + Bu can be stabilized by means of a smooth bounded control if and only if it has no eigenvalues with positive real part, and all the uncontrollable modes have a negative real part. Here, the authors investigate, for single-input systems, the question of whether such systems can be stabilized by means of a feedback u = σ(h(x)), where h is linear and σ(s) is a saturation function such as sign(s) min(|s|,1). A stabilizing feedback of this particular form exists if A has no multiple eigenvalues, and also in some other special cases such as the double integrator. It is shown that for the multiple integrator of order n, with n ≥ 3, no saturation of a linear feedback can be globally stabilizing.

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M3 - Conference contribution

AN - SCOPUS:0026673743

SN - 0780304500

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 70

EP - 72

BT - Proceedings of the IEEE Conference on Decision and Control

PB - Publ by IEEE

T2 - Proceedings of the 30th IEEE Conference on Decision and Control Part 1 (of 3)

Y2 - 11 December 1991 through 13 December 1991

ER -