Abstract
This paper addresses stability of families of linear, time‐invariant systems with single time delay. The families are generated by system parameters uncertain within known intervals, and appearing linearly (affinely) in the systems' characteristic functions, which are quasi‐polynomials. First, easily implementable conditions for delay‐independent stability for such families are given. Later, for families that fail to be stable independently of delay, a computationally tractable method is presented to compute all possible time‐delay intervals for which the families are stable. The method is based on the edge theorem and provides the complete stability picture of a given family. Numerical examples illustrate the application of the method. Copyright © 2010 John Wiley & Sons, Ltd.