线性时变时滞系统新的稳定性准则

在时滞是时变的且属于一个区间的情况下,研究了线性时滞系统的稳定性问题.基于二次类型的Lyapunov-Krasovskii泛函,利用积分的凸组合和Jensen积分不等式,给出了一个新的依赖时滞区间的稳定性判别方法.把时滞区间分段,在每段内采用适当的不等式对Lyapunov-Krasovskii泛函导数的积分项系数进行放大,避免了在不同区间上使用统一的不等式,从而减少了使用凸组合方法带来的保守性.用理论分析和数值算例证明了所得结果比现有结果具有更小的保守性.

New Stability Criteria for Linear Systems with Time-Varying Delay

On the assumption that the delay is time-varying and ranges in an interval, the stability of linear systems with a delay was studied. Based on a Lyapunov-Krasovskii functional of quadratic type, a new stability criterion dependent on the delay range was proposed by employing the convex combination of integrals and Jensen's integral inequality. Partitioning the delay range into segments, the coefficients of integral terms in the derivative of the Lyapunov-Krasovskii functional were enlarged by using appropriate inequalities for each segment. The conservatism of the convex combination method was reduced due to not using unified inequality for different segments. Theoretical analysis and numerical examples showed that the result obtained had less conservatism than that of some existing ones.