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A numerical scheme to approximate delay Lyapunov matrices for exponentially stable linear time-delay systems with distributed delay is given.

The aim is to summarize recent results on stability and robust stability of multivariate polynomials. The largets class of polynomials preserving stability when thay are subjected to small coefficient variations is recalled. Then adaptation of the zero exlcusion principle for this class is introduced. Applications of this theory are shown for the edge theorem, stability of interval families and complex structured radius, all of them for the so-called class of stable multivariate polynomials.

A special transformation of time delay systems is studied. Delay dependent stability conditions for a transformed linear time varying system with delay are compared with that of the original one. Additional stability conditions inposed by the transformation are derived.

In this survey some recent contributions to stability and robust stability analysis of linear time delay systems with parameter uncertainty are discussed. The main aim of the paper is to discuss some basic techniques used for deriving tractable stability and robust stability conditions. The reference list presents rather a small portion of the large number of publications in this field.

Given an interval quasipolynomial Q={∑k=0n∑s=1maksλn-ker,λ|aksɛ[aks,[a¯ ks]; k=o,1,...,n; s=1,2,..., m} We are looking for necessary and sufficient conditions for all quasipolynomials from Q have roots only in the open left-half plane of the complex plane.