分数布朗运动干扰下广义模糊系统的有限时间随机有界性分析

Finite-time stochastic boundedness analysis for singular fuzzy systems with fractional Brownian motions

分数布朗运动作为动力学系统中一类随机扰动的输入噪声受到越来越多学者的关注。研究了带有分数布朗运动的广义T-S模糊系统的有限时间随机有界性问题。首先提出一个带有分数布朗运动干扰的广义T-S模糊系统模型,在此基础上设计了一个模糊状态反馈控制器,然后构造了一个与分数布朗运动的Hurst指数相关的新型Lyapunov泛函,利用线性矩阵不等式得到了所研究系统有限时间随机有界的充分条件。最后通过一个数值算例验证了本文结论的有效性。

Fractional Brownian motions,as the input noise of a kind of random disturbances in dynamic system,has attracted more and more attention.In this paper,the finite-time stochastic boundedness problem for singular T-S fuzzy systems with fractional Brownian motions is studied.Firstly,a singular T-S fuzzy system model with fractional Brownian motion disturbances is proposed.On this basis,a fuzzy state feedback controller is designed.Then a new-type Lyapunov functional dependent of Hurst index of fractional Brownian motions is constructed,and sufficient conditions of the finite-time stochastic boundedness for the studied system are obtained by using linear matrix inequalities(LMI).Finally,a numerical example is given to verify the feasibility of the conclusion.