含有非线性扰动的时滞随机微分系统的鲁棒均方稳定性

摘要

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.%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It?o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.