两类Lurie时滞系统的稳定性分析与滤波器设计

发布时间：2018-06-14 09:42

  本文选题：Lurie系统 + T-S模型　； 参考：《杭州电子科技大学》2015年硕士论文

【摘要】：Lurie时滞系统是非线性控制中不可缺少的组成部分，这类系统的概念由Lurie在1944年研究一个非线性控制模型系统时提出来。这个系统可以简化成线性部分和非线性部分，线性部分用准确的模型描述，且要求稳定，非线性部分要求其为连续并且包含在由两条直线组成的扇形区域内。本文主要研究两类Lurie时滞系统的绝对稳定性分析和滤波器的设计。研究内容主要包括三个部分： 第一部分：考虑一类中立型Lurie时滞系统，这类系统带有常数混合时滞，研究其绝对稳定性问题。首先，利用时滞分解方法，将状态时滞分割为小区间，构造新型Lyapunov-Krasovskii泛函，分别在无限扇形区间的条件和有限扇形区间条件下，，运用矩阵不等式处理技巧得到系统绝对稳定的充分条件。接着，进一步深入考虑系统在带有不确定条件下，这类系统在有限扇形条件下的绝对稳定性条件。 第二部分：在状态时滞是时变情况下，考虑一类带有中立型Lurie时变系统的绝对稳定性问题。其中中立时滞是常数时滞且状态时滞是变时滞，时变时滞在一定区间内，通过对时变时滞划分成小区间，使得每个区间片段构成新的Lyapunov-Krasovskii泛函，并通过Leibniz-Newton公式引入自由权矩阵，在无限扇形区间的条件下，最后得到线性矩阵不等式形式的绝对稳定条件。 第三部分：对一类基于T-S模型的Lurie型时变时滞系统，在有限扇形条件下，研究其∞滤波问题。这个部分主要根据线性矩阵不等式技术得到时滞相关的设计结果，通过寻求一个依赖于时滞变化的Lyapunov-Krasovskii泛函，引入自由权矩阵的方法，对得到的滤波误差系统进行稳定性分析，由于在矩阵不等式中出现了耦合的矩阵变量，再利用所得结果结合矩阵解耦合的方法，使其保守性进一步降低。 每一部分内容最后，都给出相应的数例验证结果。
[Abstract]:Lurie time-delay system is an indispensable part of nonlinear control. The concept of this kind of system was proposed by Lurie when he studied a nonlinear control model system in 1944. The system can be simplified into linear part and nonlinear part. The linear part is described by an accurate model and it needs to be stable. The nonlinear part needs to be continuous and contained in a sector region composed of two straight lines. In this paper, the absolute stability analysis and filter design of two classes of Lurie time-delay systems are studied. In the first part, we consider a class of neutral Lurie time-delay systems with constant mixed delays and study its absolute stability. First of all, by using the time-delay decomposition method, the state delay is divided into small intervals, and a new Lyapunov-Krasovskii functional is constructed, under the conditions of infinite sector interval and finite sector interval, respectively. The sufficient conditions for the absolute stability of the system are obtained by using matrix inequality processing techniques. Then, the absolute stability conditions of this kind of systems under the condition of finite sector shape are further considered under the condition of uncertainty. In the second part, we consider the absolute stability of a class of Lurie time-varying systems with neutral type when the state delay is time-varying. The vertical delay is a constant delay and the state delay is a variable delay. The time-varying delay is in a certain interval. By dividing the time-varying delay into small intervals, each segment of the interval forms a new Lyapunov-Krasovskii functional, and the free right matrix is introduced by Leibniz-Newton formula. Under the condition of infinite sector interval, the absolute stability condition in the form of linear matrix inequality is obtained. Part three: for a class of Lurie time-varying time-delay systems based on T-S model, the 鈭

本文编号：2016940