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This note focuses on the static output feedback stabilization problem for a class of single-input-single-output systems when the control law includes multiple (distinct) delays. We are interested in giving necessary conditions for the existence of such stabilizing controllers. Illustrative examples (second-order system, chain of integrators, or chain of oscillators) are presented, and discussed. Index Terms--Asymptotic stability, delay, quasi-polynomial.

Quasi-polynomial families generated by multivariate interval polynomials are considered. It is shown that for these families both delay independent and delay dependent vertex-type stability conditions hold. Index Terms--Multivariate polynomials, robust stability, time-delay systems, vertex-type stability conditions.

This note focuses on the stability of some class of delay systems, including uncertainty in the delays. More precisely, we are interested in guaranteeing the stability of perturbed delay systems by assuming the stability of the nominal system. If the delay perturbation is constant, necessary and sufficient conditions are derived in terms of generalized eigen-value distribution of some (finite-dimensional) constant matrix pencil. If the delay perturbation is time-varying, some sufficient stability conditions are derived using "exact" Lyapunov--Krasovskii functionals. Illustrative examples are also included. Index Terms--Delay, Lyapunov functionals, matrix pencils, uncertainty.

There are two fundamental results available when we study stability of a polynomial family that is described by convex polytope in the coefficient space: The Edge Theorem and the theory based on the concept of convex directions. Many known results can be explained with these two results. This paper deals with a generalization of this line of research to the case of quasipolynomials that are entire functions which include both degree of the independent variable and exponential functions. The main objects of the paper are the developing of the concept of convex directions for quasipolynomials and exploiting this concept for construction of testing sets for quasipolynomial families. One of the primary sources of motivation for the class of problems considered in this paper is derived from process control. A typical problem formulation almost always includes a delay element in each subsystem process block. When we interconnect a number of such blocks in a feedback system, the study of robust stability involves quasipolynomials of the sort considered in this paper.