线性多时滞系统的稳定性分析

Stability analysis of linear multiple time delay systems

讨论了以微分－ 差分方程描述的线性多时滞系统的渐近稳定性问题． 综合利用Ｌｙａｐｕｎｏｖ 函数方法，结合矩阵测度和矩阵范数的性质， 通过加强不等式， 给出线性多时滞系统时滞无关渐近稳定的新的充分条件． 这些条件既可用于判断系统的稳定性， 又可用于估计系统中不确定参数的界限； 同时它们又是线性单时滞系统的稳定性判别条件的推广．

This paper discusses the problem of asymptotic stability for the linear systems with multiple time delay. Applying Lyapunov function method and the property of the matrix measure and the matrix norm, some new sufficient conditions for asymptotic stable independent of delay of the linear systems with multiple time delay are presented. These conditions can be used to determine the stability of the systems and to estimate the bounds of the uncertain parameters in the systems. They are the extension of the stability conditions for the linear systems with single time delay. Finally, we illustrate that, for the case of single time delay, the conservatism of our results is less than those given in the literature.