TY - JOUR

T1 - Equivalence between classes of multipliers for slope-restricted nonlinearities

AU - Carrasco, J.

AU - Heath, W.P.

AU - Lanzon, A.

PY - 2013/6/1

Y1 - 2013/6/1

N2 - Different classes of multipliers have been proposed in the literature for obtaining stability criteria using passivity theory, integral quadratic constraint (IQC) theory or Lyapunov theory. Some of these classes of multipliers can be applied with slope-restricted nonlinearities. In this paper the concept of phase-containment is defined and it is shown that several classes are phase-contained within the class of Zames–Falb multipliers. There are two main consequences: firstly it follows that the class of Zames–Falb multipliers remains, to date, the widest class of available multipliers for slope-restricted nonlinearities; secondly further restrictions may be avoided when exploiting the parametrization of the other classes of multipliers.

AB - Different classes of multipliers have been proposed in the literature for obtaining stability criteria using passivity theory, integral quadratic constraint (IQC) theory or Lyapunov theory. Some of these classes of multipliers can be applied with slope-restricted nonlinearities. In this paper the concept of phase-containment is defined and it is shown that several classes are phase-contained within the class of Zames–Falb multipliers. There are two main consequences: firstly it follows that the class of Zames–Falb multipliers remains, to date, the widest class of available multipliers for slope-restricted nonlinearities; secondly further restrictions may be avoided when exploiting the parametrization of the other classes of multipliers.

U2 - 10.1016/j.automatica.2013.02.012

DO - 10.1016/j.automatica.2013.02.012

M3 - Erthygl

VL - 49

SP - 1732

EP - 1740

JO - Automatica

JF - Automatica

IS - 6

ER -