TY - JOUR

T1 - Concise stability conditions for systems with static nonlinear feedback expressed by a quadratic program

AU - Li, G.

AU - Heath, W.P.

AU - Lennox, B.

PY - 2008/7/1

Y1 - 2008/7/1

N2 - The stability of the feedback connection of a strictly proper linear time-invariant stable system with a static nonlinearity expressed by a convex quadratic program (QP) is considered. From the Karush-Kuhn–Tucker conditions for the QP, quadratic constraints that may be used with a quadratic Lyapunov function to construct a stability criterion via the S-procedure are established. The approach is based on existing results in the literature, but gives a more parsimonious linear matrix inequality (LMI) criterion and is much easier to implement. This approach can be extended to model predictive control and gives equivalent results to those in the literature but with a much lower dimension LMI criterion

AB - The stability of the feedback connection of a strictly proper linear time-invariant stable system with a static nonlinearity expressed by a convex quadratic program (QP) is considered. From the Karush-Kuhn–Tucker conditions for the QP, quadratic constraints that may be used with a quadratic Lyapunov function to construct a stability criterion via the S-procedure are established. The approach is based on existing results in the literature, but gives a more parsimonious linear matrix inequality (LMI) criterion and is much easier to implement. This approach can be extended to model predictive control and gives equivalent results to those in the literature but with a much lower dimension LMI criterion

U2 - 10.1049/iet-cta:20070225

DO - 10.1049/iet-cta:20070225

M3 - Erthygl

VL - 2

SP - 554

EP - 563

JO - IET Control Theory and Applications

JF - IET Control Theory and Applications

IS - 7

ER -