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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April 2019
Research-Article
Full-Order and Reduced-Order Exponential Observers for Discrete-Time Nonlinear Systems With Incremental Quadratic Constraints
Wei Zhang,
Wei Zhang
Laboratory of Intelligent Control and Robotics,
Shanghai University of Engineering Science,
Shanghai 201620, China
e-mail: wizzhang@foxmail.com
Shanghai University of Engineering Science,
Shanghai 201620, China
e-mail: wizzhang@foxmail.com
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Younan Zhao,
Younan Zhao
Laboratory of Intelligent Control and Robotics,
Shanghai University of Engineering Science,
Shanghai 201620, China
e-mail: younan.zhao@foxmail.com
Shanghai University of Engineering Science,
Shanghai 201620, China
e-mail: younan.zhao@foxmail.com
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Masoud Abbaszadeh,
Masoud Abbaszadeh
Lead Control Systems Engineer
Model-Based Controls Lab,
GE Global Research,
Niskayuna, NY 12309
e-mail: masouda@ualberta.ca
Model-Based Controls Lab,
GE Global Research,
Niskayuna, NY 12309
e-mail: masouda@ualberta.ca
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Mingming Ji
Mingming Ji
Lecturer
Laboratory of Intelligent Control and Robotics,
Shanghai University of Engineering Science,
Shanghai 201620, China
e-mail: jimingming923@163.com
Laboratory of Intelligent Control and Robotics,
Shanghai University of Engineering Science,
Shanghai 201620, China
e-mail: jimingming923@163.com
Search for other works by this author on:
Wei Zhang
Laboratory of Intelligent Control and Robotics,
Shanghai University of Engineering Science,
Shanghai 201620, China
e-mail: wizzhang@foxmail.com
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
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
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
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. Apr 2019, 141(4): 041005 (9 pages)
Published Online: December 6, 2018
Article history
Received:
April 8, 2018
Revised:
October 4, 2018
Citation
Zhang, W., Zhao, Y., Abbaszadeh, M., and Ji, M. (December 6, 2018). "Full-Order and Reduced-Order Exponential Observers for Discrete-Time Nonlinear Systems With Incremental Quadratic Constraints." ASME. J. Dyn. Sys., Meas., Control. April 2019; 141(4): 041005. https://doi.org/10.1115/1.4041712
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