一类区间时变输入时滞与状态时滞线性系统的稳定性研究

Stabilization analysis of interval time-varying state and input delays systems

研究一类具有区间时变输入时滞与状态时滞线性系统的稳定性问题.通过选择合理的Lyapunov-Krasovskii函数,基于积分等式方法(积分等式由自由权矩阵构造而成),以LMI的形式给出时滞相关的稳定性充分条件,并进行了相关控制器的设计.所得结论对时滞导数没有任何限制,可用于快时变时滞系统.同时,积分等式方法较积分不等式方法更优,保守性更低.最后,通过数值比较及仿真表明了所提出方法的有效性和优越性.

This paper considers the stabilization of interval time-varying State and input delays systems. Based on appropriate Lyapunov-Krasovskii function and integral equality approach, in which integral equality is constructed with free weighting matrices, the sufficient conditions for delay-dependent stabilization are derived in terms of LMI and the controller is also designed. The results have no restriction on the derivatives of the time-varying delay and can be applied to quick time-varying delays systems. At the same time, the new improved integral equality approach is much less conservative than integral inequality approach. Finally, the numerical example and simulation show the effectiveness and feasibility of the method.