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In this contribution we present an extension of the prediction scheme proposed in Manitius and Olbrot (1979) for the compensation of the input delay to the case of linear neutral type systems with input delay. For simplicity of the presentation we treat the case of systems with one state delay. [ABSTRACT FROM AUTHOR]

Abstract: In this contribution we present an extension of the prediction scheme proposed in Manitius and Olbrot (1979) for the compensation of the input delay to the case of linear systems with both input delay and state delay. For simplicity of the presentation we treat the case of systems with one state delay. [Copyright &y& Elsevier]

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]

Abstract: A necessary and sufficient condition for the existence and uniqueness of Lyapunov matrices for neutral type single delay systems is presented. [Copyright &y& Elsevier]

Abstract: In this contribution we present some basic results concerning the computation of quadratic functionals with prescribed time derivatives for linear time delay systems. Some lower and upper bounds for the functionals are given. The functionals are defined by special matrix valued functions. These functions are called Lyapunov matrices. The theory of the matrices is a rather young topic. Therefore, principal results with respect to the existence and uniqueness of the matrices are included. Some important applications of the functionals are pointed out. A brief historical survey ends the contribution. [Copyright &y& Elsevier]

Focuses on quasi-polynomial families generated by multivariate interval polynomials and derives a class of polytopic families of quasi-polynomials for which the stability of a finite number of vertex quasi-polynomials implies that of the whole family as of November 2003. Overview of quasi-polynomials and multivariate polynomials; Relationship between stability of a multivariate polynomial and that of the generated quasi-polynomial; Glimpse of basic definitions for families of multivariate polynomials and quasi-polynomials.

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]