The Zames-Falb IQC for systems with integrators

Author

Jönsson, U. ; Megretski, A.

Author_Institution

Lab. for Inf. & Decision Syst., MIT, Cambridge, MA, USA

Volume

45

Issue

3

fYear

2000

fDate

3/1/2000 12:00:00 AM

Firstpage

560

Lastpage

565

Abstract

A feedback interconnection of a neutrally stable, linear time-invariant system and a nonlinearity with 0⩽xφ(x)⩽kx² is called critical because the worst case linearization is at best neutrally stable. This characteristic makes the stability analysis of such systems particularly hard. It is shown that an integrator and a sector bounded nonlinearity can be encapsulated in a bounded operator that satisfies several useful integral quadratic constraints, which gives powerful tools for stability analysis of a general class of critically stable systems

Keywords

Popov criterion; control nonlinearities; control system analysis; feedback; linear systems; robust control; Zames-Falb integral quadratic constraints; bounded operator; critically stable systems; feedback interconnection; neutrally stable linear time-invariant system; sector bounded nonlinearity; stability analysis; worst case linearization; Automatic generation control; Hydraulic actuators; Impedance matching; Neck; Perturbation methods; Pneumatic actuators; Shape memory alloys; Vibration control; Wires;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.847744

Filename

847744