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Abstract: 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 such that 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. [Copyright &y& Elsevier]

Abstract: In this contribution, we study Lyapunov matrices for a time-delay system. The main contribution consists in the demonstration that the set of matrix equations that defines the matrices admit a unique solution if the spectrum of the time-delay system does not contain a point , such that also belongs to the spectrum. [Copyright &y& Elsevier]

In this paper, some recent results on additional dynamics for transformed time-delay systems are extended to the case of time-varying systems. Special equations which describe these dynamics are derived. Additional restrictions on stability and robust stability imposed by the transformations are obtained. [Copyright &y& Elsevier]