Robust stability for noncommensurate time-delay systems

Based on the maximum principle and some properties of matrix measure and matrix norm, several new stability criteria for perturbed multiple noncommensurate time-delays systems are proposed. These criteria ensure all roots of the system's characteristic equation lying on or to the left of Re(s) = -a, a > o. Two approaches are used here, one is a direct test which needs some matrix computations and the other is a loci test in which one needs to draw the loci of eigenvalues. With the aid of convex combination property, the restricted region where unstable characteristic roots of the system locate could be estimated accurately.