Asymptotic stability and stabilisation of uncertain delta operator systems with time-varying delays
Asymptotic stability and stabilisation of uncertain delta operator systems with time-varying delays
复制标题
DOI：
10.1049/iet-cta.2012.0749
复制
发表时间：
2013-05
影响因子：
2.6
通讯作者：
Xiaochen Xie;Shen Yin;Huijun Gao;O. Kaynak
中科院分区：
文献类型：
--
作者：
Xiaochen Xie;Shen Yin;Huijun Gao;O. Kaynak
本文主要研究基于Delta算子方法的不确定线性变时滞系统的渐近稳定性和镇定问题。通过采用一种新的模型公式，时滞Delta算子系统被转化为一个互联系统的不确定性可以变得容易处理。基于时滞状态的两项近似和尺度小增益定理，利用一种新的Lyapunov-Krasovskii泛函，建立了一类不确定Delta算子时滞系统鲁棒渐近稳定和状态反馈镇定的时滞相关充分条件.所获得的标准统一了一些以前提出的相关方法，在文献中看到的实现渐近稳定和稳定的连续和离散系统到三角洲算子框架。数值算例表明了所提方法的优越性和有效性。
This study focuses on the asymptotic stability and stabilisation of uncertain linear systems with time-varying delays via delta operator approach. By employing a new model formulation, the time-delayed delta operator system is transformed into an interconnected system for which the uncertainties can become easy to deal with. Based on a two-term approximation of delayed state and scaled small gain theorem, new delay-dependent sufficient conditions of robust asymptotic stability and state-feedback stabilisation of an uncertain delta operator time-delayed system are established by using a novel Lyapunov-Krasovskii functional. The criteria obtained unify some previously suggested relevant methods seen in literature for achieving asymptotic stability and stabilisation of both continuous and discrete systems into the delta operator framework. Numerical examples presented explicitly demonstrate the advantages and effectiveness of the proposed methods.