Circuits, Systems, and Signal Processing

, Volume 37, Issue 9, pp 3725–3738 | Cite as

Exponential Reduced-Order Observers for Nonlinear Systems Satisfying Incremental Quadratic Constraints

  • Younan Zhao
  • Wei ZhangEmail author
  • Wuyang Zhang
  • Fang Song


This paper considers the design problem of exponential reduced-order observers for nonlinear systems satisfying incremental quadratic constraints governed by an incremental multiplier matrix. Sufficient existence conditions of the exponential full-order observers are established and formulated in terms of matrix inequalities. Then, it is shown that the conditions under which an exponential full-order observer exists also guarantee the existence of an exponential reduced-order observer. Moreover, with a proper parameterization of the multiplier matrix, the design of reduced-order observers is reduced to solving linear matrix inequalities of the Lyapunov matrix and observer gain matrices. Finally, the effectiveness of the proposed design method is illustrated by an example.


Observer design Nonlinear systems Reduced-order observers Incremental quadratic constraints Linear matrix inequalities 



This work was supported in part by the National Natural Science Foundation of China under Grant 51505273, the State Key Laboratory of Robotics and System (HIT) under Grant SKLRS-2014-MS-10, the Jiangsu Provincial Key Laboratory of Advanced Robotics Fund Projects under Grant JAR201401 and the Fund of MOE Key Laboratory of Image Processing and Intelligence Control (Huazhong University of Science and Technology) under Grant No. IPIC2015-02.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Laboratory of Intelligent Control and RoboticsShanghai University of Engineering ScienceShanghaiChina
  2. 2.MOE Key Laboratory of Image Processing and Intelligence ControlHuazhong University of Science and TechnologyWuhanChina
  3. 3.State Key Laboratory of Robotics and SystemHarbin Institute of TechnologyHarbinChina

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