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Technical Brief

Stabilization of Discrete-Time Linear Systems With Quantization and Noise Input

[+] Author and Article Information
Mingming Ji

Department of Automation,
Shanghai Jiao Tong University,
Key Laboratory of System Control and Information Processing,
Ministry of Education of China,
Shanghai 200240, China
e-mail: jimingming923@163.com

Chunyu Yang

School of Information and Electrical Engineering,
China University of Mining and Technology,
Xuzhou 221116, China
e-mail: chunyuyang@cumt.edu.cn

Weidong Zhang

Department of Automation,
Shanghai Jiao Tong University,
Key Laboratory of System Control and Information Processing,
Ministry of Education of China,
Shanghai 200240, China
e-mail: wdzhang@sjtu.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 March 7, 2014; final manuscript received October 29, 2014; published online January 27, 2015. Assoc. Editor: Jwu-Sheng Hu.

J. Dyn. Sys., Meas., Control 137(6), 064502 (Jun 01, 2015) (5 pages) Paper No: DS-14-1103; doi: 10.1115/1.4029031 History: Received March 07, 2014; Revised October 29, 2014; Online January 27, 2015

In this paper, our main concern is the problem of stabilization of discrete-time linear systems with both quantization and noise input. Stabilizability by means of quantizers that perform adaptations called “zooming” is analyzed. The noise input can be separated into an additive white noise part and a deterministic constant input disturbance. The analysis of mean-square stability of the system with noise input is essentially the asymptotic stability of the system disturbed by a constant input. It is shown that the system with the constant input disturbance is asymptotically stabilized by the quantized feedback control policy if the system without noise input can be stabilized by a linear state feedback law. Both the state quantization and the input quantization are studied.

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Figures

Grahic Jump Location
Fig. 1

An inverted pendulum system with quantized state feedback

Grahic Jump Location
Fig. 2

State response of system (53)

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