研究一类多面体不确定切换线性系统的鲁棒1_2—1_∞滤波器设计问题。基于参数依赖的Lypunov函数,通过引入松弛矩阵,实现了Lyapunov矩阵和系统矩阵的解耦,从而减小了设计的保守性。利用线性矩阵不等式技术得到了滤波器存在的充分条件,并给出滤波器矩阵的求解方法。算例验证了所给方法的有效性。 A robust 1_2-1_∞ filter design problem for a class of switched linear systems with uncertain switched polytopics is studied. Based on the Lypunov function with parameter dependence, the relaxation matrix is ​​introduced to realize the decoupling of the Lyapunov matrix and the system matrix, which reduces the conservativeness of the design. The sufficient condition of the existence of the filter is obtained by using the linear matrix inequality technique and the method of solving the filter matrix is ​​given. The example verifies the effectiveness of the given method.