具概率分布变时滞随机系统鲁棒稳定性

Robust delay-probability-distribution stability of linear stochastic systems with time-varying delay

本文研究了一类有非线性时变随机时滞的线性不确定系统的鲁棒稳定性.其中时变随机时滞表征为伯努利随机过程,具有已知的概率分布和变化范围.通过构造新泛函,建立了基于线性矩阵不等式的鲁棒均方指数稳定的充分条件,此条件易于用MATLAB工具箱来验证.本文所获得结果的主要特征是稳定性条件依赖时滞的概率分布和时滞导数的上界.同时也证明了允许时变随机时滞的时滞比之传统的确定性时滞有更大的变化范围,因此我们的条件比确定性时滞更为保守.算例表明了文中所提方法的有效性.

This paper is concerned with the robust stability of a class of linear uncertain stochastic systems with non- linear time-varying stochastic time-delay which is characterized by a Bernoulli stochastic process with given distribution probability in a given variation range. By constructing a new Lyapunov-Krasovskii functional, we derive for the system the sufficient conditions of mean-square exponential stability in terms of the linear matrix inequalities（LMIs）, which can be checked readily by using MATLAB toolbox. The feature of our results is the conclusion of stability conditions being dependent not only on the probability distribution of the time-delay, but also on the upper bound of the its derivative. Mean- while, we also show that the allowable variation range of the time-varying stochastic time-delay can be greater than that of a deterministic time-delay in ensuring the same stability; this demonstrates the less conservativeness of our requirements than the traditional ones. An example is given to illustrate the effectiveness of the proposed method.