L2-gain analysis and feedback design for discontinuous time-delay systems based on functional differential inclusion
L2-gain analysis and feedback design for discontinuous time-delay systems based on functional differential inclusion
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DOI：
10.1109/cdc.2009.5399660
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发表时间：
2009-12
期刊：
影响因子：
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通讯作者：
Jiangyan Zhang;T. Shen;Xiaohong Jiao
中科院分区：
文献类型：
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作者：
Jiangyan Zhang;T. Shen;Xiaohong Jiao
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L2增益分析和反馈控制问题的方法。受右端不连续微分方程的Filippov解的启发，引入了受外信号强迫的不连续时滞系统的定义，并给出了在解概念意义下的L2-增益性质的描述.然后，基于时滞相关的偏微分不等式，给出了一个条件，使得给定的不连续时滞系统的L2-增益小于给定的水平，且无强迫系统在Filippov解意义下是稳定的.利用该条件，给出了一种状态反馈控制器的设计方法，使得闭环系统满足L2增益约束和渐近稳定性。数值例子来证明所提出的理论结果。
A functional differential inclusion-based approach to L2-gain analysis and feedback control problems is presented for a class of discontinuous time-delay systems. Motivated by Filippov solution in the differential equations with discontinuous right-hand side, definition of the discontinuous time-delay systems forced by external signals is introduced, and a description of L2-gain property in the sense of the solution concept is given. Then, a condition such that a given discontinuous time-delay system has L2-gain less than a given level and the unforced system is stable in the sense of Filippov solution is presented based on a delay-dependent partial differential inequality. Furthermore, using the presented condition, a design method of state feedback controller is shown such that the closed-loop system satisfies the L2-gain constraint and asymptotical stability. Numerical examples are presented to demonstrate the presented theoretical results.