ROBUST STABILITY OF TIME-DELAY SYSTEMS

There are two fundamental results available when we study stability of a polynomial family that is described by convex polytope in the coeff icient spare: The Edge Theorem and the theory based on the concept of convex direction. Many known results can be explained with these two r esults. This paper deals with a generalization of this line of researc h to the case of quasipolynomials that are entire functions which incl ude both degree of the independent variable and exponential functions. The main objects of the paper are the developing of the concept of co nvex directions for quasipolynomials and exploiting this concept for c onstruction of testing sets for quasipolynomial families. One of the p rimary sources of motivation for the class of problems considered in t his paper is derived from process control. A typical problem formulati on almost always includes a delay element in each subsystem process bl ock. When we interconnect a number of such blocks in a feedback system , the study of robust stability involves quasipolymonials of the sort considered in this paper.