# American Institute of Mathematical Sciences

November  2020, 16(6): 2799-2812. doi: 10.3934/jimo.2019081

## A robust reduced-order observers design approach for linear discrete periodic systems

 1 Institute of Electric Power, North China University of Water Resources and Electric Power, Zhengzhou 450011, China 2 Key Laboratory of Big Data Analysis and Processing of Henan Province, Henan University, Zhengzhou 450011, China

*Corresponding author: Lei Zhang

Received  October 2018 Revised  March 2019 Published  November 2020 Early access  July 2019

Fund Project: This work is supported by the Programs of National Natural Science Foundation of China (Nos. U1604148, 11501200, 61402149), Innovative Talents of Higher Learning Institutions of Henan (No. 17HASTIT023), Central China thousand talents program(No.ZYQR201810138)

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.

Citation: Lingling Lv, Wei He, Xianxing Liu, Lei Zhang. A robust reduced-order observers design approach for linear discrete periodic systems. Journal of Industrial & Management Optimization, 2020, 16 (6) : 2799-2812. doi: 10.3934/jimo.2019081
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##### References:
The trajectories of observed state errors by $L_{t}^{\mathrm{rand}}$ and $L_{t}^{\mathrm{robu}}$
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