On the stability of a certain class of nonlinear sampled-data systems

Author

Jury, E.I. ; Lee, B.W.

Author_Institution

University of California, Berkeley, CA, USA

Volume

9

Issue

1

fYear

1964

fDate

1/1/1964 12:00:00 AM

Firstpage

51

Lastpage

61

Abstract

A sufficient condition for stability of a class of sampled-data feedback systems containing a memory-less, nonlinear gain element is obtained. The new stability theorem for the class of systems discussed requires that the following relationship be satisfied on the unit circle: $\\Re G^{\\ast }(z)[1 + q(z - 1)] + frac{1}{K} - frac{K\´|q|}{2} | (z - 1)G^{\\ast }(z)|^{2} \\leq 0$ . In this papers the stability criterion embodied in this theorem can be readily obtained from the frequency response of the linear plant. This method is essentially similar to Popov\´s method applied to the study of nonlinear continuous systems. Furthermore, Tsypkin\´s resuits for the discrete case are obtained as a special case when $q=0$ . Several examples are discussed, and the results are compared with Lyapunov\´s quadratic and quadratic plus integral forms as well as with other methods. For these examples, the results obtained from the new theorem yield less conservative values of gain than Lyapunov\´s method. Furthermore, for certain linear plants the new theorem also yields the necessary and sufficient conditions.

Keywords

Discrete-time systems, nonlinear; Nonlinear systems, discrete-time; Stability; Automatic control; Continuous time systems; Control systems; Feedback; Frequency response; Lyapunov method; Sampled data systems; Space exploration; Stability criteria; Sufficient conditions;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.1964.1105622

Filename

1105622