不确定时滞摄动滤波误差动态系统的稳定性分析  

Stability Analysis of Uncertain Singularly Perturbed Filter Error Dynamic Systems With Time Delays

作　　者：孙凤琪[1] SUN Fengqi(College of Mathematics,Jilin Normal University,Siping,Jilin 136000,P.R.China)

机构地区：[1]吉林师范大学数学学院,吉林四平136000

出　　处：《应用数学和力学》2020年第8期899-911,共13页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(61741318)。

摘　　要：基于Lyapunov稳定性理论、线性矩阵不等式方法、时滞分段分析方法、自由权矩阵方法、矩阵分析方法等,该文在前期滤波器设计理论基础上,进一步研究了含有不确定性结构的时变时滞奇异摄动滤波误差动态系统的稳定性分析问题.通过构造新的Lyapunov泛函,引用新的交叉项界定法并根据系统特性,推出了时滞依赖和时滞独立两种情形下新的滤波误差动态系统稳定性判别条件.最后,给出数值样例表明该文所得结果的有效性和可行性.With the Lyapunov stability theory,the linear matrix inequality method,the time delay piecewise analysis method,the matrix analysis method and the free weight matrix method,the stability of singularly perturbed filter error dynamic systems with time-varying delays and uncertain structures was studied on the basis of the previous filter design theory.Through construction of a new Lyapunov function,with a new cross-term definition method and according to the system characteristics,a new criterion for stability of filter error dynamic systems in 2 cases of time delay dependence and time delay independence was derived.Finally,the selected numerical example illustrates the effectiveness and feasibility of the obtained results.

关 键 词：滤波误差动态系统 线性矩阵不等式(LMI) 时滞系统 时滞依赖 时滞独立 不确定系统 滤波器设计 LYAPUNOV-KRASOVSKII泛函 

分 类 号：O231.2[理学—运筹学与控制论]