A nonlinear small gain theorem for the analysis of control systems with saturation

Author

Teel, Andrew R.

Author_Institution

Dept. of Electr. Eng., Minnesota Univ., Minneapolis, MN, USA

Volume

41

Issue

9

fYear

1996

fDate

9/1/1996 12:00:00 AM

Firstpage

1256

Lastpage

1270

Abstract

A nonlinear small gain theorem is presented that provides a formalism for analyzing the behavior of certain control systems that contain or utilize saturation. The theorem is used to show that an iterative procedure can be derived for controlling systems in a general nonlinear, feedforward form. This result, in turn, is applied to the control of: 1) linear systems (stable and unstable) with inputs subject to magnitude and rate saturation and time delays; 2) the cascade of globally asymptotically stable nonlinear systems with certain linear systems (those that are stabilizable, right invertible, and such that all of their invariant zeros have nonpositive real part); 3) the inverted pendulum on a cart; and 4) the planar vertical takeoff and landing aircraft

Keywords

aircraft control; asymptotic stability; control system analysis; feedforward; linear systems; nonlinear control systems; poles and zeros; cart; feedforward; globally asymptotically stable nonlinear systems; inverted pendulum; iterative procedure; linear systems; nonlinear small gain theorem; planar vertical takeoff and landing aircraft; right invertible systems; saturation; unstable systems; Asymptotic stability; Control system analysis; Control systems; Feedback; Lyapunov method; Nonlinear control systems; Nonlinear equations; Nonlinear systems; Stability analysis;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.536496

Filename

536496