Time-Varying Halanay Inequalities With Application to Stability and Control of Delayed Stochastic Systems
Time-Varying Halanay Inequalities With Application to Stability and Control of Delayed Stochastic Systems
复制标题
时变 Halanay 不等式及其在时滞随机系统稳定性和控制中的应用
DOI：
10.1109/tac.2021.3061986
复制
发表时间：
2022-03
影响因子：
6.8
通讯作者：
Feiqi Deng
中科院分区：
文献类型：
--
作者：
Xueyan Zhao;Feiqi Deng
本文在简单自然的条件下，将Halanay不等式推广到时变形式，不需要常数来限定时变系数。通过与系数和时滞相关联的可行函数对来估计基本不等式解。给出了典型特殊情况下的推论。给出了搜索初始可行偶的几种方法，并提出了一种优化可行偶的迭代算法。数值算例和仿真结果表明了所得结果的实用性和优越性。作为基础，首先研究了具有任意变时滞的泛函微分不等式和方程的比较原理。作为主要结果的应用，研究了具有时变系数和时滞的随机系统的稳定性和控制问题，主要考虑了系统的时间方差。建立了一个渐近稳定性定理和一个判据，并提出了一种有趣的无界时滞控制策略，即基于受电弓时滞采样数据的反馈控制策略。给出了稳定性判据和控制策略，并用数值实验进行了验证。
In this article, the Halanay inequality is generalized into the time-varying version under simple and natural conditions, without constant to bound the time-varying coefficients. The solution of the underlying inequality is estimated by virtue of the feasible function pair associated with the coefficients and delays. Corollaries are given for typical special cases. Some approaches are illustrated for the searching of the initial feasible pairs, and an iterative procedure is proposed for the optimization of the feasible pairs. The usage and superiority of the obtained result are exhibited by numerical examples with simulations. As a base, the comparison principle for the functional differential inequalities and equations with arbitrary time-varying delays is studied first. As an application of the main result, the stability and control of the stochastic systems with time-varying coefficients and delays are investigated, with the main concern to the time variance. An asymptotic stability theorem and a criterion are established, and an interesting control strategy with unbounded time delay, namely the pantograph delay sampled data based feedback, is proposed. The stability criterion and the control strategy are illustrated and verified with numerical experiments.