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含有非线性扰动的时滞随机微分系统的鲁棒均方稳定性
引用本文:柴双龙,李树勇.含有非线性扰动的时滞随机微分系统的鲁棒均方稳定性[J].工程数学学报,2017,34(4).
作者姓名:柴双龙  李树勇
作者单位:绵阳师范学院数理学院,绵阳,621050
基金项目:国家自然科学基金(11271270). The National Natural Science Foundation of China
摘    要:研究一类含有非线性扰动的多时变时滞随机微分系统在有记忆状态的反馈控制器下的鲁棒均方稳定性问题.通过构造Lyapunov-Krasovskii泛函,运用Ito公式,引入适当的自由权矩阵,利用积分不等式和分析技巧,基于线性不等式(LMI)方法和Schur补定理,获得含该系统的鲁棒均方渐近稳定和鲁棒均方指数稳定,并给出了相应反馈控制器设计.所得结果与时滞和随机干扰相关,丰富了已有的结果.

关 键 词:非线性扰动  时滞随机微分系统  反馈控制  线性矩阵不等式  鲁棒均方稳定

Robust Mean Square Stability for Stochastic Differential Delay Systems with Nonlinear Perturbation
CHAI Shuang-long,LI Shu-yong.Robust Mean Square Stability for Stochastic Differential Delay Systems with Nonlinear Perturbation[J].Chinese Journal of Engineering Mathematics,2017,34(4).
Authors:CHAI Shuang-long  LI Shu-yong
Abstract:This paper is concerned with the robust mean square stability for stochastic differ-ential systems with multiple time-varying delays and nonlinear perturbation in memory state feedback controller. By establishing a Lyapunov-Krasovskii functional, using the It?o formula, introducing appropriate free-weighting matrices, making use of an integral inequality and an analytical technique, based on the linear matrix inequality (LMI) and Schur complement theo-rem, the robust mean square asymptotically stability and the robust mean square exponentially stability for the system are obtained. In addition, the corresponding state feedback controllers are constructed. The results are dependent on delays and stochastic perturbation, and extend the existing results.
Keywords:nonlinear perturbation  stochastic differential system with delays  feedback con-trol  linear matrix inequality (LMI)  robust mean square stability
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