Frequency-domain instability criteria for time-varying and nonlinear systems
- 1 May 1967
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in Proceedings of the IEEE
- Vol. 55 (5) , 604-619
- https://doi.org/10.1109/proc.1967.5626
Abstract
Recent research has produced a number of frequency-domain stability criteria applicable to linear systems having nonlinear and/or time-varying feedback. One of the more interesting of these stability criteria is the so-called Circle Criterion which represents a generalization of the familiar result of Nyquist. The present paper provides a basis for generating instability counterparts of most of the available frequency-domain stability criteria. The procedure is described in detail for the Circle Criterion. Once the general pattern is established it becomes a simple matter to generate instability counterparts of other similar stability criteria. Several worked examples are included to illustrate the theory. The paper has been written with both the general reader and the specialist in mind; it is hoped that both will find something of interest.Keywords
This publication has 18 references indexed in Scilit:
- Stability of control systems with multiple nonlinearitiesJournal of the Franklin Institute, 1966
- 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
- Some Results on the Theory of Physical Systems Governed Nonlinear Functional EquationsBell System Technical Journal, 1965
- On the Boundedness of Solutions of Nonlinear Integral EquationsBell System Technical Journal, 1965
- On the Existence of Lyapunov Function for the Problem of Lur’eJournal of the Society for Industrial and Applied Mathematics Series A Control, 1965
- On the Stability of Nonlinear Feedback SystemsIEEE Transactions on Applications and Industry, 1964
- A Frequency-Domain Condition for the Stability of Feedback Systems Containing a Single Time-Varying Nonlinear ElementBell System Technical Journal, 1964
- On the Stability of Solutions of Linear Differential Equations with Periodic CoefficientsJournal of the Society for Industrial and Applied Mathematics, 1964
- LYAPUNOV FUNCTIONS FOR THE PROBLEM OF LUR'E IN AUTOMATIC CONTROLProceedings of the National Academy of Sciences, 1963
- Positive Real MatricesIndiana University Mathematics Journal, 1960