Critical frequencies and parameters for linear delay systems: A Lyapunov matrix approach

A new method, based on recent results concerning the construction of the Lyapunov matrix of delay systems, reveals conditions under which the characteristic function has a root s0s0 such that −s0−s0 is also a root. As the pure imaginary roots, which are crucial in the stability analysis of time delay systems, are of that type, this method gives rise to a novel approach for the delay independent and delay dependent stability analyses of systems with delay that are multiple of a basic delay, distributed delays and of a class of neutral type time delay systems. A number of examples are given to illustrate the approach and to show its strength.