New phase plane for determining limit cycles and stability of digital systems
by
Qihong Ke

A kind of phase plane for digital systems is presented in this paper. Here, digital systems can be digital control systems or digital filters, both linear and non-linear ones. For digital systems with constant input under arbitrary initial conditions, the phase plane can show the existence, the position and the magnitude of limit cycles, and also the states locus and the stability directly. Limit cycles are non-linear, and resulted from the finite word length and recursive calculation. They reduce the performance of the systems. Based on the Phase Plane, to eliminate limit cycles and to improve the stability is just to adjust system parameters individually, which makes the design of digital systems easy and direct. Balance Line is developed in the Phase Plane to determine limit cycles and the stability of digital systems. Criteria for searching limit cycles in Phase Plane have been established. Circles in which all limit cycles will be located are presented. The Phase Plane also shows that the magnitude of constant input will affect limit cycles. Three Theorems are given to determine limit cycles and the stability of digital systems.

Date received: January 31, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cago-30.