具有时变时滞的线性离散系统的稳定性新判据

A new criterion for stability of discrete-time systems with time-varying state delay

讨论了含有时变状态时滞的离散时间的系统稳定性问题。通过定义一个恰当的Lyapunov泛函,并利用改进的自由权矩阵方法,结合一些不等式处理交叉乘积项定界问题,得到了一个新的时滞相关的渐近稳定判据。该判据用线性矩阵不等式的形式给出,其优点在于降低了现有文献结论的保守性。最后给出数值例子,说明本文结果的有效性和优越性。

This paper is concerned with the stability analysis of discrete-tlme systems with time-varying state delay. By defining an appropriate Lyapunov-Krasovskii functional and by employing the developed free weight matrices technique to achieve delay dependence and by utilizing some bounding inequalities for cross products between two vectors, a sufficient condition is derived in term of the linear matrix inequalities. The merit of the proposed condition lies in their less conservativeness. Finally, a numerical example is given to demonstrate effectiveness of the proposed method.