Encirclement conditions for stability and instability of feedback systems with delays†

Abstract

This paper gives necessary and sufficient conditions for the input-output stability of several classes of time invariant feedback systems involving time delays in the loop. Criteria are given which utilize only the ‘real frequency’ behaviour of the transfer functions involved and require what may be interpreted as the satisfaction of two separate encirclement conditions. The results are applicable to both scalar and multiple input systems with a stable open loop, and to scalar systems with an unstable open loop.

Notes

† Communicated by the Author.