【摘要】 针对离散时变时滞系统的稳定性问题,采用改进型离散Wirtinger不等式方法进行研究,获得了一个保守性更低的稳定性判据.首先构造了一个新的辅助向量函数,利用正定矩阵的二次型都是正值的特性,提出了改进型Wirtinger不等式,获得了比传统的方法如离散Jensen不等式、离散Wirtinger不等式更好的求和逼近结果.在此基础上,构建了合适的Lyapunov-Krasovskii泛函,应用改进型离散Wirtinger不等式从而获得有更低保守性的稳定性判据,最终利用两个数值仿真完成验证.验证结果表明,利用新方法得到的时滞上界要大于现有的不等式方法,更接近理论值,从而表明了本文方法的有效性和优越性.更多还原

【Abstract】 In view of the stability analysis of linear discrete systems, an intense research has been conducted by adopting an improved discrete Wirtinger-based inequality. A new stability criterion of linear discrete systems with interval time-varying delay is derived, which yields less conservative stability conditions. By definition of a novel auxiliary function, we propose a better integral inequality and receive a tighter stability condition as compared to the recently results such as discrete Jensen inequality, discrete Wirtinger-based inequality. Based on the new inequality, we construct a dedicated Lyapunov-Krasovskii functional and obtain a tighter estimation of the derivative of Lyapunov-Krasovskii functional in terms of the new inequality. Finally, two numerical examples are given to demonstrate the efficiency of our new methods.更多还原