一类线性时滞系统的时滞依赖稳定性研究

针对一类带有参数不确定性的线性时滞系统,研究其时滞依赖稳定性问题。采用改进的Lyapunov-Krasovskii泛函方法给出了线性时滞系统基于线性矩阵不等式的时滞依赖稳定的充分条件,在定理的证明中结合牛顿公式改进了一系列二次型积分不等式,从而有效降低了定理保守性。最后给出2个计算实例,通过与现有方法的比较可以看出本文方法的更加有效,且得到的最大时滞具有更小的保守性。

Delay-dependent Criteria for Robust Stability of Uncertain Linear Systems

The linear time-delayed systems with parameter uncertainty was focused on and the problem of their asymptotical stability was studied. First, using Lyapunov-Krasovskii functional method, the sufficient conditions of delay-dependent stability based on linear matrix inequality (LMI) were derived to ensure that linear systems with time delay are asymptotically stable. Then, in the proof of the theorems, combined with Leibniz-Newton formula a series of quadratic integral inequalities were improved. Therefore the conservativeness of the theorems was reduced efficiently. Last, two examples were given to illustrate that the new methods are more effective than the present methods and the delay bounds obtained are of less conservative.