On robust stability of uncertain systems with multiple time‐delays

Abstract

AbstractOn the basis of an infinite to one mapping and the structure of the null space of a multivariate matrix polynomial (MMP), a novel sufficient condition is derived in this paper for the robust stability of a linear time‐invariant system with multiple uncertain time‐delays, parametric modelling errors and unmodelled dynamics. This condition depends on time‐delay bounds and is less conservative than the existing ones. An attractive property is that this condition becomes also necessary in some physically meaningful situations, such as the case that there is only one uncertain time‐delay and neither parametric perturbations nor unmodelling errors exist. Moreover, using ideas of representing a positive‐definite MMP through matrix sum of squares, an asymptotic necessary and sufficient condition is derived for the robust stability of this system. All the conditions can be converted to linear matrix inequalities. Copyright © 2009 John Wiley & Sons, Ltd.