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研究了一类复杂非线性系统的有限时间H∞滤波问题。针对由Takagi-Sugeno模糊模型描述的复杂非线性系统,同时考虑其存在参数不确定性以及时变时滞的情形,给出系统有限时间有界的充分条件。在一般传统H∞滤波器设计的基础上,结合有限时间有界的概念,导出保证系统在有限时间内,其滤波误差能量小于一个给定上界的H∞滤波器设计方法。通过构造一个适当的Lyapunov-Krasovskii函数,并引入自由权矩阵,得到基于线性矩阵不等式的有限时间H∞滤波器参数的求解方法。自由权矩阵的引入,是一种处理时变时滞项的新方法,具有一定的研究价值。最后,通过仿真示例验证了该方法的有效性。
The finite-time H∞ filtering problem for a class of complex nonlinear systems is studied. Aiming at the complex nonlinear system described by Takagi-Sugeno fuzzy model, the existence of parametric uncertainties and time-varying delays are considered simultaneously, and sufficient conditions for the bounded finite system to be given are given. Based on the traditional H∞ filter design, combined with the concept of finite time boundedness, an H∞ filter design method is proposed to guarantee the system’s filtering error energy less than a given upper bound in a finite time. By constructing an appropriate Lyapunov-Krasovskii function and introducing a free-weight matrix, a finite-time H∞ filter parameter solution based on linear matrix inequality (LMI) is obtained. The introduction of the free-weights matrix is a new method to deal with time-varying time-lag items and has certain research value. Finally, the simulation results show the effectiveness of the method.