不确定离散时间系统的变增益H_2/H_∞滤波

Gain-scheduled H2/H∞ filtering for uncertain discrete-time systems

研究凸多面体不确定离散时间系统的变增益H2/H∞滤波器设计问题.通过引入附加松弛变量,提出一种新的Lyapunov矩阵与系统矩阵解耦的混合H2/H∞性能准则.基于该性能准则,推导了变增益H2/H∞滤波器存在的充分条件,并将滤波器设计问题转化为具有线性矩阵不等式约束的凸优化问题.仿真结果表明了所提出方法的有效性.

The design problem of gain-scheduled H2/H∞ filter for polytopic discrete-time systems is investigated. By introducing additional slack variables, a new mixed H2/H∞ performance criterion is proposed, which provides the decoupling between Lyapunov matrix and system matrices. Based on the proposed performance criterion, a sufficient condition for the existence of gain-scheduled H2/H∞ filter is derived. Furthermore, the filter design problem is converted into a convex optimization problem with linear matrix inequality constraints. Simulation results show the effectiveness of the proposed design approach.