This paper investigates the problem of designing reduced-order observers for linear discrete-time periodic (LDP) systems. In case that the linear discrete-time periodic system is observable, an algebraic equivalent system is obtained by non-singular linear transformation, and the partial states to be observed are separated simultaneously. Then the considered problem is transformed into the problem of solving a class of periodic Sylvester matrix equation and an iterative algorithm for periodic reduced-order state observers design is derived. In addition, robust consideration based on periodic reduced-order state observers for LDP systems is also conducted. At last, one numerical example is worked out to illustrate the effectiveness of the proposed approaches.

中文翻译：

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线性离散周期系统的鲁棒降阶观测器设计方法

本文研究了为线性离散时间周期（LDP）系统设计降阶观测器的问题。在可观察到线性离散时间周期系统的情况下，通过非奇异线性变换获得代数等效系统，并且将要观察的部分状态同时分离。然后将考虑的问题转化为求解一类周期Sylvester矩阵方程的问题，并推导了用于周期降阶状态观测器设计的迭代算法。另外，还针对LDP系统进行了基于周期性降序状态观察器的健壮考虑。最后，通过算例说明了所提方法的有效性。