具有时滞和的非线性系统的鲁棒稳定性分析

Robust stability analysis of nonlinear systems with two additive time-varying delay components

针对具有时滞和及模有界参数不确定性的非线性系统,研究了鲁棒稳定性问题。通过构造新的Lyapunov泛函,其中考虑了时变时滞和时滞上界信息,并应用新的方法估计Lyapunov泛函导数的上界,以线性矩阵不等式形式给出了系统的时滞相关型稳定性判据。数值实例表明了结果的有效性和较小保守性。

This paper considers the problem of robust stability of nonlinear systems with two additive time-varying delay components and norm-bounded parameter uncertainties. Based on a new Lyapunov functional, which takes the relationship between the time-varying delay and its upper bound into account and using a new approach to estimating the upper bound on the time derivative of the Lyapunov functional, a delay-dependent stability criterion of the system is established in terms of linear matrix inequalities （LMIs）. Numerical examples are given to illustrate that the obtained results are effective and have less conservatism.