一类非线性时滞系统的时滞相关稳定性分析

Analysis on Stabilization for a Kind of Nonlinear Time-varying Delay System

针对一类非线性时变时滞系统,基于T-S模糊模型,采用自由权矩阵的方法,研究了该系统的稳定性问题。设计了一个与系统状态变量的导数有关的模糊控制器,推导出该控制器使闭环系统渐近稳定的充分条件,该条件等价于一类线性矩阵不等式（LMI）的可解性,并以仿真算例证明了控制器的有效性。

This paper is concerned with the problem of stabilization for nonlinear system with time-varying delay.The problem is solved by using free-weighting-matrix approach based on the T-S fuzzy model.A delay-dependent fuzzy controller is designed related to the system state variable and a sufficient condition is given so that the system with time-varying delay is asymptotically stable.The sufficient condition is equivalent to the solvability of a kind of linear matrix inequality（LMI）.Simulation results show the effectiveness of the proposed method.