TY - GEN

T1 - Finite-time stabilization of uncertain SISO systems

AU - Levant, Arie

PY - 2007

Y1 - 2007

N2 - Any uncertain smooth single-input single-output dynamic system of the full relative degree can be locally finitetime stabilized at its equilibrium point by means of a standard continuous feedback. High-order sliding-mode approach is modified for this sake, and a list of continuous controllers is built depending only on the given relative degree n of the system output σ. Provided the relative degree is globally well-defined and the system growth rate is restricted, the global finite-time stabilization is possible. The asymptotic accuracies in the cases of discrete and noisy sampling are estimated. In particular, for any q > 0 the stabilization accuracy σ(i) = O(τn-i+q), i = 0, 1, ..., n - 1, is obtained, where τ is the sampling interval, and q is an arbitrarily chosen positive feedback parameter. Outputfeedback controllers are constructed. Computer simulation confirms the applicability of the approach.

AB - Any uncertain smooth single-input single-output dynamic system of the full relative degree can be locally finitetime stabilized at its equilibrium point by means of a standard continuous feedback. High-order sliding-mode approach is modified for this sake, and a list of continuous controllers is built depending only on the given relative degree n of the system output σ. Provided the relative degree is globally well-defined and the system growth rate is restricted, the global finite-time stabilization is possible. The asymptotic accuracies in the cases of discrete and noisy sampling are estimated. In particular, for any q > 0 the stabilization accuracy σ(i) = O(τn-i+q), i = 0, 1, ..., n - 1, is obtained, where τ is the sampling interval, and q is an arbitrarily chosen positive feedback parameter. Outputfeedback controllers are constructed. Computer simulation confirms the applicability of the approach.

UR - http://www.scopus.com/inward/record.url?scp=62749139647&partnerID=8YFLogxK

U2 - 10.1109/CDC.2007.4434393

DO - 10.1109/CDC.2007.4434393

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AN - SCOPUS:62749139647

SN - 1424414989

SN - 9781424414987

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 1728

EP - 1733

BT - Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 46th IEEE Conference on Decision and Control 2007, CDC

Y2 - 12 December 2007 through 14 December 2007

ER -