Connections between Georgiou and Smith's robust stability type theorems and the nonlinear small-gain theorems

TY - JOUR

T1 - Connections between Georgiou and Smith's robust stability type theorems and the nonlinear small-gain theorems

AU - Li, Jing

AU - French, Mark

PY - 2021/6/1

Y1 - 2021/6/1

N2 - Georgiou and Smith's robust stability theorem using the concept of nonlinear gap metric is shown to be equivalent to the traditional nonlinear small-gain theorem for feedback systems with parts of zero input disturbances. We present both global and local forms of the nonlinear small-gain theorem establishing existence and boundedness properties simultaneously in this paper; and the results are used to show the corresponding types of Georgiou and Smith's robust stability theorem.

AB - Georgiou and Smith's robust stability theorem using the concept of nonlinear gap metric is shown to be equivalent to the traditional nonlinear small-gain theorem for feedback systems with parts of zero input disturbances. We present both global and local forms of the nonlinear small-gain theorem establishing existence and boundedness properties simultaneously in this paper; and the results are used to show the corresponding types of Georgiou and Smith's robust stability theorem.

KW - nonlinear small-gain theorem, robust stability theorem, nonlinear gap metric, schauder's fixed point theorem

U2 - 10.1137/19M1285500

DO - 10.1137/19M1285500

M3 - Article

SN - 0363-0129

VL - 59

SP - 1989

EP - 2010

JO - SIAM JOURNAL ON CONTROL AND OPTIMIZATION

JF - SIAM JOURNAL ON CONTROL AND OPTIMIZATION

IS - 3

ER -