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给出了一种离散系统最优滤波器的线性矩阵不等式（ＬＭＩ） 设计方法。在系统干扰噪声能量有界情况下， 将有约束的滤波问题转换为无约束的最优状态估计问题。利用ＬＭＩ方法给出了最优无偏滤波器存在的充分必要条件， 所得滤波器的阶数小于系统状态个数。将ＬＭＩ方法应用于飞机飞行试验数据处理中， 分析了实际飞行条件下飞机运动的模型， 并对该模型进行扩展线性化处理， 得到了一个较易实现的ＬＭＩ滤波算法。仿真结果表明， 所提出的算法是可行的。
A linear matrix inequality (LMI) design method for the optimal system of discrete systems is given. Under the circumstance that the system interference noise energy is bounded, the constrained filtering problem is transformed into an unconstrained optimal state estimation problem. The LMI method is used to give the necessary and sufficient conditions for the existence of an optimal unbiased filter. The order of the resulting filter is smaller than the number of states of the system. The LMI method is applied to the data processing of aircraft flight test, the model of aircraft movement under actual flight conditions is analyzed, and the extended linearization of the model is carried out. A LMI filtering algorithm which is easy to implement is obtained. Simulation results show that the proposed algorithm is feasible.