Dither in nonlinear systems
- 1 October 1976
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 21 (5), 660-667
- https://doi.org/10.1109/tac.1976.1101357
Abstract
A dither is a high-frequency signal introduced into a nonlinear system with the object of augmenting stability. In this paper,[1] it is shown that the effects of dither depend on its amplitude distribution function. The stability of a dithered system is related to that of an equivalent smoothed system, whose nonlinear element is the convolution of the dither distribution and the original nonlinearity. The ability of dithers to stabilize large classes of nonlinear systems is explained in terms of an effective narrowing of the nonlinear sector. A feature of the approach taken here is that a deterministic (i.e., strong) concept of stability is established under probabilistic (i.e., weak) assumptions on the dither.Keywords
This publication has 6 references indexed in Scilit:
- Feedback Systems: Input-Output PropertiesJournal of Dynamic Systems, Measurement, and Control, 1975
- The Analysis of Feedback SystemsPublished by MIT Press ,1971
- Functional AnalysisPublished by Springer Nature ,1968
- On the input-output stability of time-varying nonlinear feedback systems--Part II: Conditions involving circles in the frequency plane and sector nonlinearitiesIEEE Transactions on Automatic Control, 1966
- On the input-output stability of time-varying nonlinear feedback systems Part one: Conditions derived using concepts of loop gain, conicity, and positivityIEEE Transactions on Automatic Control, 1966
- Haskins's Momental Theorem and Its Connection with Stieltjes's Problem of MomentsTransactions of the American Mathematical Society, 1917