连续线性不确定时滞系统的时滞分布和时滞区间相关的鲁棒指数均方稳定性判据

摘要

解决了一类时滞服从二项分布的连续线性不确定时滞系统的鲁棒稳定性问题.利用李雅普诺夫稳定性理论和线性矩阵不等式方法,给出改进的该类系统的时滞分布和时滞区间相关的鲁棒指数均方稳定性判据.判据以线性矩阵不等式形式给出,方便于使用MATLAB软件中的LMI工具箱求解.理论的和数值的比较表明所提出判据比文献中的具有更小保守性.%Robust exponential mean square stability problem for a class of continuous-time linear uncertain time-delay systems is considered. The delay is a random variable observing binary distribution. Using Lyapunov stability theory and linear matrix inequality method, an improved delay-distribution-dependent and delay-interval-dependent exponential mean square stability criterion for this class of systems is proposed. The given stability criterion is of the form of linear matrix inequalities, which can be conveniently solved by the LMI toolbox of MATLAB. The results of theoretical and numerical comparisons show that the criterion proposed in this paper is less conservative than those in literature.