α-Stability analysis of perturbed systems with multiple noncommensurate time delays

In terms of the fundamental matrix and the Jordan canonical form of the system matrix A₀, a new and simple α-stability criterion for multiple noncommensurate time-delay systems is proposed. The criterion is sufficient to ensure that all roots of the system´s characteristic equation lie to the left of Re(s)=-α, α⩾0 and is also extended to the delay systems with parametric perturbations. It will be seen that if α is not equal to zero, the corresponding stability criteria depend on the delay time