General Formulation of the Nyquist Criterion
- 1 June 1965
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Circuit Theory
- Vol. 12 (2), 230-234
- https://doi.org/10.1109/tct.1965.1082403
Abstract
The Nyquist diagram technique is examined under very general assumptions; in particular, the linear subsystem is represented by a convolution operator, thus, the case of any linear time-invariant distributed circuit is included. It is shown that if there are no encirclements of the critical point, then the impulse response of the closed-loop system is bounded and absolutely integrable on[0, \infty); it also tends to zero ast \rightarrow \infty. For any initial state, the zero-input response of the closed-loop system is also bounded and goes to zero. If, on the other hand, there are one or more encirclements of the critical point, then the closed-loop impulse response tends asymptotically to a growing exponential.Keywords
This publication has 4 references indexed in Scilit:
- A generalization of the Popov criterionIEEE Transactions on Automatic Control, 1965
- A Frequency-Domain Condition for the Stability of Feedback Systems Containing a Single Time-Varying Nonlinear ElementBell System Technical Journal, 1964
- Handbuch der Laplace-TransformationPublished by Springer Science and Business Media LLC ,1950
- Regeneration TheoryBell System Technical Journal, 1932