TY - JOUR

T1 - Robust Stability of Time-Delay Systems

AU - Kharitonov, Vladimir L.

AU - Zhabko, Alexei P.

PY - 1994/1/1

Y1 - 1994/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0028727242&partnerID=8YFLogxK

U2 - 10.1109/9.362855

DO - 10.1109/9.362855

M3 - Letter

AN - SCOPUS:0028727242

VL - 39

SP - 2388

EP - 2397

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

SN - 0018-9286

IS - 12

ER -