基于Finsler引理的一类连续时间多时滞系统稳定性分析

Stability Analysis of a Class of Continuous Time Systems with Multiple Delays Based on Finsler Lemma

针对具有多个变时滞的系统,为简化其稳定性判据,首先将动力学方程转化为代数方程,其次运用Finsler引理给出系统稳定的新的判别定理,然后构造Lyapunov-Krasovskii泛函对定理进行严格的数学证明。在此基础上,选择合适的正交补矩阵对稳定性条件作进一步简化。最后通过2个数值算例对结论进行验证。结果表明:给出的定理可简单有效地判别带有多个变时滞系统的稳定性。

For systems with multiple time-varying delays,in order to simplify the stability criterion,firstly,the dynamic equation is transformed into an algebraic equation.Secondly,a new criterion theorem for system stability is given by using Finsler lemma,and then a Lyapunov-Krasovskii functional is constructed to prove the theorem strictly.On this basis,an appropriate orthogonal complement matrix is selected to further simplify the stability condition.Finally,the conclusion is verified by two numerical examples.The results show that the theorem given in this paper can simply and effectively judge the stability of systems with multiple time-varying delays.