Feedback stabilization of a class of time-delay systems with discontinuity: A functional differential inclusion-based approach
Feedback stabilization of a class of time-delay systems with discontinuity: A functional differential inclusion-based approach
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DOI：
10.1109/iccas.2008.4694338
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发表时间：
2008-10
期刊：
影响因子：
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通讯作者：
Jiangyan Zhang;T. Shen
中科院分区：
文献类型：
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作者：
Jiangyan Zhang;T. Shen
针对一类不连续时滞系统，提出了一种基于泛函微分包含的反馈镇定方法。通过将Filippov意义下的微分包含推广到泛函微分包含，给出了满足Filippov集值泛函的不连续时滞系统解的概念.利用这一概念，证明了Lyapunov-Krasovskii稳定性定理和LaSalle不变性原理可以很容易地推广到讨论具有不连续性的时滞系统的稳定性问题.基于所介绍的分析工具，证明了一类非线性时滞系统的反馈镇定控制器可以使闭环系统强渐近稳定.数值例子的仿真结果证明了所提出的控制方法。
In this paper, a feedback stabilization approach is proposed for a class of time-delay systems with discontinuity based on functional differential inclusions. By extending the differential inclusion in the sense of Filippov to functional differential inclusion, a notion of the solution for time-delay systems with discontinuity is presented that is defined satisfying the proposed Filippov set-valued functional. With this notion, it is shown that both the Lyapunov-Krasovskii stability theorem and the LaSalle invariance principle can be easily extended to discuss the stability problem of time-delay systems with discontinuity. Based on the introduced analysis tools, it is proved that a feedback stabilization controller can be obtained for a class of nonlinear time-delay systems with discontinuity such that the closed loop system is strongly asymptotically stable. Simulation result of a numerical example is given to demonstrate the proposed control approach.