A local form of small gain theorem and analysis of feedback Volterra systems

Author

Zheng, Qingsheng ; Zafiriou, Evanghelos

Author_Institution

Dept. of Chem. Eng., Maryland Univ., College Park, MD, USA

Volume

44

Issue

3

fYear

1999

fDate

3/1/1999 12:00:00 AM

Firstpage

635

Lastpage

640

Abstract

The requirement of evaluating a gain over the entire signal space is one of the restrictions in the traditional small gain theorem. In this paper, a local form of small gain theorem is presented. It yields a bound on the external signal that guarantees that the magnitude of the specified signal along the closed loop stays within a certain region and hence it is useful in addressing the signal magnitude dependent stability problem. The theorem is used to analyze the feedback properties of a Volterra series system as well as an inverse (or pseudo inverse) Volterra system. Improvement over existing results is demonstrated, both theoretically and via numerical examples

Keywords

Volterra series; closed loop systems; control system analysis; feedback; inverse problems; nonlinear systems; stability; Volterra series system; closed loop; external signal bound; feedback Volterra system analysis; pseudo inverse Volterra system; signal magnitude dependent stability problem; small gain theorem; Feedback; Information analysis; Nonlinear control systems; Nonlinear dynamical systems; Nonlinear systems; Polynomials; Process control; Robust control; Robust stability; Signal analysis;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.751367

Filename

751367