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Technical Brief

Reduced-Order Observer Design for Discrete-Time Descriptor Systems With Unknown Inputs: An Linear Matrix Inequality Approach

[+] Author and Article Information
Shenghui Guo

College of Electronics and Information Engineering, Tongji University,
Shanghai 201804, China;
Suzhou University of Science and Technology,
Suzhou 215009, China
e-mail: 12gsh@tongji.edu.cn

Fanglai Zhu

College of Electronics and Information Engineering,
Tongji University,
Shanghai 201804, China
e-mail: zhufanglai@tongji.edu.cn

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received June 18, 2014; final manuscript received April 2, 2015; published online May 26, 2015. Assoc. Editor: Yongchun Fang.

J. Dyn. Sys., Meas., Control 137(8), 084503 (Aug 01, 2015) (7 pages) Paper No: DS-14-1261; doi: 10.1115/1.4030336 History: Received June 18, 2014; Revised April 02, 2015; Online May 26, 2015

Reduced-order observer design methods for both linear and nonlinear discrete-time descriptor systems based on the linear matrix inequality (LMI) approach are investigated. We conclude that the conditions under which a full-order observer exists can also guarantee the existence of a reduced-order observer. By choosing a special reduced-order observer gain matrix, a reduced-order unknown input observer is proposed for linear system with unknown inputs, and then an unknown input reconstruction is provided for some special cases. We also extend above results to the cases of nonlinear systems. Finally, three numerical comparative simulation examples are given to illustrate the effectiveness and merits of proposed methods.

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Figures

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Fig. 1

States estimation of reduced-order (plus) and full-order observers (dashed)

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Fig. 2

States estimation of reduced-order (plus) and full-order observers (dashed)

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Fig. 3

Unknown input reconstruction (dashed)

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Fig. 4

States estimation of reduced-order (plus) and full-order observers (dashed) (η(k)≡0)

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Fig. 5

States estimation of reduced-order (plus) and full-order observers (dashed) (η(k)≠0)

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Fig. 6

Unknown input reconstruction (dashed)

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