一类有界区间时变时滞系统的稳定性分析与研究

Stability Analysis on Interval Time-varying State Delay Systems

研究一类具有区间时变状态时滞的系统的稳定性问题.通过选择合理的Lyapunov-Krasovskii泛函,基于积分等式法(积分等式由自由权矩阵构造而成),以LMI(线性矩阵不等式)的形式给出时滞相关的稳定性充分条件.本文方法对时变时滞的导数没有任何限制,适用于快时变时滞系统.而且积分等式法比积分不等式方法保守性更低.最后通过仿真及数值算例说明了本文方法的有效性和优越性.

The stability of the interval time-varying delay systems is considered. By choosing the appropriate Lyapunov-Krasovskii functional, the sufficient conditions of delay-dependent stabilization are derived in terms of LMI （linear matrix inequality） based on integral equality approach （integral equality is constructed with free weighting matrices）. There is no restriction on the derivative of the time-varying delay in the method, and it can be applied to the systems with quickly time-varying delays. Moreover, the integral equality approach possess much lower conservatism than the integral inequality approach. Finally, the simulation and numeric example prove that the method is effective and superior.