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research-article

Full-order and Reduced-order Exponential Observers for Discrete-time Nonlinear Systems with Incremental Quadratic Constraints

[+] Author and Article Information
Wei Zhang

Associate Professor, Laboratory of Intelligent Control and Robotics, Shanghai University of Engineering Science, Shanghai, 201620, China
wizzhang@foxmail.com

Younan Zhao

Master Student, Laboratory of Intelligent Control and Robotics, Shanghai University of Engineering Science, Shanghai, 201620, China
younan.zhao@foxmail.com

Masoud Abbaszadeh

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

Mingming Ji

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

1Corresponding author.

ASME doi:10.1115/1.4041712 History: Received April 08, 2018; Revised October 04, 2018

Abstract

This paper considers the observer design problem for a class of discrete-time system whose nonlinear time-varying terms satisfying 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.

Copyright (c) 2018 by ASME
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