具有随机时滞的区间时滞系统稳定性分析

Stability Analysis of Interval-time-varying Delay Systems with Stochastic Delay

研究一类具有随机时滞的时变时滞系统的稳定性问题。首先,假设时变时滞在2个区间的概率分布是已知的,通过引入1个服从伯努利分布的随机变量来描述时变时滞在第1个区间的取值概率,系统被转化为一类概率区间时变时滞系统;其次,为了充分利用时滞信息,在构造的Lyapunov-Krasovskii(L-K)泛函中引入增广矩阵和三重积分项;然后,通过Wirtinger积分不等式和凸组合相结合的方法来处理L-K泛函求导过程中出现的二次型积分项,并以线性矩阵不等式的形式给出一个保守性较小的稳定性准则。最后,通过数值示例验证方法的有效性。

The problem of stability for a class of systems with random time-varying delay is investigated in this paper.Firstly,it is assumed that the probability distributions of the delay in two intervals are known in priori.A Bernoulli distribution random variable is introduced to describe the probability of time-varying delay in the first interval,and the original systems are transformed into a class of systems with probabilistic interval time-varying delay.Secondly,in order to make full use of the information of the probability distribution of the delay,an augmented matrix and triple integral terms are included in the Lyapunov-Krasovskii(L-K)functional.Then,by employing Wirtinger integral inequality and convex combination method,the quadratic integral terms from the infinitesimal operator of L-K is handled,a less conservative stability criterion for the system is formulated in the form of linear matrix inequalities.Finally,two numerical examples are given to verify the effectiveness of the proposed method.