Necessary conditions of exponential stability for a class of linear uncertain systems with a single constant delay |
| |
| Authors: | Xian Zhang Xinxiao Liu Yantao Wang Xin Wang |
| |
| Institution: | 1. School of Mathematical Science, Heilongjiang University, Harbin 150080, PR China;2. Heilongjiang Provincial Key Laboratory of the Theory and Computation of Complex Systems, Heilongjiang University, Harbin 150080, PR China |
| |
| Abstract: | In this paper, we will investigate the necessary conditions, described by the Lyapunov matrix, for the robust exponential stability for a class of linear uncertain systems with a single constant delay and time-invariant parametric uncertainties, which are some generalizations of the existing results on uncertain linear time-delay systems. As a medium step, several pivotal properties of parameter-dependent Lyapunov matrix are proposed, which set up the relationships between fundamental matrix and Lyapunov matrix for the considered system. In addition, to calculate the parameter-dependent Lyapunov matrix, we introduce the differential equation method and the Lagrange interpolation method, respectively. Furthermore, it is noted that the proposed necessary conditions can be used to estimate the range of time delay, when the linear uncertain time-delay system is robust exponential stability. Finally, the validity of the obtained theoretical results is illustrated via numerical examples. |
| |
| Keywords: | Corresponding author at: School of Mathematical Science Heilongjiang University Harbin 150080 PR China |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
