不确定关联时滞系统的鲁棒H_∞滤波

Robust H-infinity filtering for uncertain interconnected time-delay systems

考虑一类不确定关联时滞系统,其中的不确定性满足范数有界条件,以子系统输出作为输入,分别为每个子系统设计一个线性滤波器.通过将系统的状态向量和滤波误差向量组合成一个新的增广向量,原系统状态方程和滤波误差方程就可以组成一个新的增广系统.如果可以设计滤波器参数,使得干扰噪声到增广系统输出的增益为最小,则噪声对系统估计的影响也就降为最低,受噪声影响的状态向量就可以恢复出来.这样,原系统的滤波问题就转化为最小化增广系统增益问题.通过选择一个适当的Lyapunov函数,并基于Lyapunov稳定性定理,得到了滤波器存在的充分条件.为了简化滤波器设计过程,将上述充分条件的未知参数矩阵定义为一个新的变换矩阵,在此基础上,实施了一系列巧妙的矩阵等价变换,同时定义了几个新的矩阵变量,将原充分条件化成了一组易于求解的线性矩阵不等式(LMI).使用Matlab的LMI工具箱,可以对上述LMIs直接求解,最后的数值算例验证了所给设计方法的有效性.

A class of uncertain interconnected time-delay systems is considered in the paper, where the uncertainties are assumed to satisfy the boundedness condition of the norm. For such a class of systems, a linear filter is designed for each subsystem by using the outputs of subsystems as inputs. With the new augmented vector composed of both the state vector and the filtering error vector, a new augmented system is derived containing the system state equations and filtering error equations. If the filter parameters can be designed to minimize the gain from disturbance noise to augmented system output, the influence of noise on the state estimate is the lowest, and the real state can be resumed at the same time. Under such conditions, the problem of filtering for the original system is equivalent to minimizing H-infinity gain of the augmented system. By selecting a proper Lya-punov function, the sufficient conditions for existence of the filter are derived on the basis of the Lyapunov stability theorem. In order to simplify the process of designing filter parameters, a new matrix transformation is introduced for the uncertain parameter matrices in sufficient conditions, and via a series of equivalent transformations, the above sufficient conditions are transformed to a system of easily solvable LMIs. Based on the LMI toolbox of Matlab software, these LMIs are directly solved. Finally, the numerical simulation proves the validity of the main results.