Criteria for stability in approximate delay systems
The authors consider the system of ordinary differential equations with constant delay \(\tau>0\) \[ x'(t)= Ax(t)+ Bx(t-\tau),\quad t\geq 0,\tag{1} \] and constant matrices \(A, B\in \mathbb{R}^{n\times n}\). They use some theorem on asymptotic stability due to \textit{T. Mori} [IEEE Trans. Autom. Control AC-30, 158-161 (1985; Zbl 0557.93058)]. This theorem requires solving transcendent equations and cannot be applied in real time to (1). The aim of the paper is a construction of an approximate system to (1) such that the asymptotic stability for this approximation implies the same property for (1). The asymptotic stability conditions on the approximate system are simplified and can be computed. Two examples are given.
linear systems of ordinary differential equations
scientific article; zbMATH DE number 1429544
scientific article