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Research Papers

Full-Order and Reduced-Order Exponential Observers for Discrete-Time Nonlinear Systems With Incremental Quadratic Constraints

[+] Author and Article Information
Wei Zhang

Laboratory of Intelligent Control and Robotics,
Shanghai University of Engineering Science,
Shanghai 201620, China
e-mail: wizzhang@foxmail.com

Younan Zhao

Laboratory of Intelligent Control and Robotics,
Shanghai University of Engineering Science,
Shanghai 201620, China
e-mail: younan.zhao@foxmail.com

Masoud Abbaszadeh

Lead Control Systems Engineer
Model-Based Controls Lab,
GE Global Research,
Niskayuna, NY 12309
e-mail: masouda@ualberta.ca

Mingming Ji

Lecturer
Laboratory of Intelligent Control and Robotics,
Shanghai University of Engineering Science,
Shanghai 201620, China
e-mail: jimingming923@163.com

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received April 8, 2018; final manuscript received October 4, 2018; published online December 6, 2018. Assoc. Editor: Yunjun Xu.

J. Dyn. Sys., Meas., Control 141(4), 041005 (Dec 06, 2018) (9 pages) Paper No: DS-18-1164; doi: 10.1115/1.4041712 History: Received April 08, 2018; Revised October 04, 2018

This paper considers the observer design problem for a class of discrete-time system whose nonlinear time-varying terms satisfy incremental quadratic constraints. We first construct a circle criterion based full-order observer by injecting output estimation error into the observer nonlinear terms. We also construct a reduced-order observer to estimate the unmeasured system state. The proposed observers guarantee exponential convergence of the state estimation error to zero. The design of the proposed observers is reduced to solving a set of linear matrix inequalities. It is proved that the conditions under which a full-order observer exists also guarantee the existence of a reduced-order observer. Compared to some previous results in the literature, this work considers a larger class of nonlinearities and unifies some related observer designs for discrete-time nonlinear systems. Finally, a numerical example is included to illustrate the effectiveness of the proposed design.

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Figures

Grahic Jump Location
Fig. 1

The state x and the estimation of x using the exponential full-order observer (15)

Grahic Jump Location
Fig. 2

Estimation error of the exponential full-order observer (15)

Grahic Jump Location
Fig. 3

Estimation error of the exponential reduced-order observer (45)

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