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Robust stability of time-delay systems

机译：时滞系统的强大稳定性

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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
机译：当研究系数空间中由凸多面形描述的多项式族的稳定性时，有两个基本结果可用：边定理和基于凸方向概念的理论。这两个结果可以解释许多已知的结果。本文将这方面的研究概括为拟多项式的情况，这些拟多项式是包括自变量程度和指数函数在内的全部函数。本文的主要目的是发展拟多项式的凸方向概念，并利用该概念构建拟多项式族的测试集。本文考虑的这类问题的主要动机之一是过程控制。典型的问题表述几乎总是在每个子系统过程块中都包含一个延迟元素。当我们在反馈系统中互连多个此类模块时，鲁棒稳定性的研究涉及本文考虑的那种拟多项式

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