2-D离散模糊系统的分析与控制
发布时间：2018-08-19 06:10
【摘要】：本文主要探究了几类2-D离散模糊系统的稳定问题,对系统的稳定性进行了分析,并设计了针对不同系统的状态反馈控制器和输出反馈控制器。由于2-D离散模糊系统依赖两个变量变化,若直接采用处理1-D系统的方法,将不能得到有效的结果,而对其较好的处理方法就是在两个变量变化的方向上分别选取不同的Lyapunov函数。其主要内容可分为下面三个部分:第一部分主要对一类2-D离散模糊系统,设计了状态反馈控制器。该部分所采用的不确定性为带有线性分式不确定情况,这包含了范数有界不确定性,具有更一般的意义。通过引入一个自由权矩阵,采用并行分布补偿方法,将当前状态和控制输入看作两个独立变量,设计出的状态反馈控制器能够使得该类系统渐近稳定。最后利用凸优化方法得到了状态反馈控制器增益。第二部分主要对一类2-D离散模糊系统,设计了输出反馈控制器和H_∞输出反馈控制。输出反馈控制作为控制系统设计中的一种重要方法在该部分得到了充分的研究,不仅考虑了确定2-D系统的输出反馈控制和具有H_∞性能指标的输出反馈控制,还考虑了包括不确定2-D系统在内的输出反馈控制和H_∞输出反馈控制。通过对系统矩阵进行奇异值分解,有效地解决了反馈增益矩阵与系统矩阵间的耦合关系,使得输出反馈控制器增益可以通过求解一系列矩阵不等式而得到。在H_∞性能作为衡量一个系统抑制干扰的重要指标情况下,本章中所设计的H_∞输出反馈控制器能够实现系统对干扰的抑制。第三部分主要针对一类2-D离散随机模糊系统,设计了H_∞状态反馈控制器。首先,2-D离散随机模糊系统是把FM第二模型中的系统矩阵扩展成随机矩阵而得到的,随机矩阵中新添加的项可以看成是对系统矩阵的随机扰动。其次,利用Lyapunov函数方法,引入自由权矩阵,建立了满足给定性能指标并使得系统均方渐近稳定的充分条件。最后,通过仿真例子证明了所得结果的正确性。
[Abstract]:In this paper, the stability problems of 2-D discrete fuzzy systems are discussed, the stability of the systems is analyzed, and the state feedback controllers and output feedback controllers for different systems are designed. Because 2-D discrete fuzzy system depends on two variables, if the method of dealing with 1-D system is adopted directly, the effective result can not be obtained, and the better way to deal with it is to select different Lyapunov functions in the direction of the change of the two variables. The main contents can be divided into the following three parts: in the first part, a state feedback controller is designed for a class of 2-D discrete fuzzy systems. The uncertainty used in this part is the uncertainty with linear fractions which contains norm-bounded uncertainties and has a more general meaning. By introducing a free right matrix and using a parallel distributed compensation method, the current state and the control input are regarded as two independent variables. The designed state feedback controller can make the system asymptotically stable. Finally, the state feedback controller gain is obtained by convex optimization method. In the second part, the output feedback controller and H _ 鈭，
本文编号：2190880
[Abstract]:In this paper, the stability problems of 2-D discrete fuzzy systems are discussed, the stability of the systems is analyzed, and the state feedback controllers and output feedback controllers for different systems are designed. Because 2-D discrete fuzzy system depends on two variables, if the method of dealing with 1-D system is adopted directly, the effective result can not be obtained, and the better way to deal with it is to select different Lyapunov functions in the direction of the change of the two variables. The main contents can be divided into the following three parts: in the first part, a state feedback controller is designed for a class of 2-D discrete fuzzy systems. The uncertainty used in this part is the uncertainty with linear fractions which contains norm-bounded uncertainties and has a more general meaning. By introducing a free right matrix and using a parallel distributed compensation method, the current state and the control input are regarded as two independent variables. The designed state feedback controller can make the system asymptotically stable. Finally, the state feedback controller gain is obtained by convex optimization method. In the second part, the output feedback controller and H _ 鈭，
本文编号：2190880
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