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Fuzzy Observer, Fuzzy Controller Design, and Common Hurwitz Matrices for a Class of Uncertain Nonlinear Systems

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Stability and Control of Nonlinear Time-varying Systems

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Abstract

In the chapter, fuzzy state observers and fuzzy controllers are developed for a type of uncertain nonlinear systems. The systems are represented by more general fuzzy modeling. Many interesting results are obtained as follows: First, by constructing Lyapunov function approaches and inequalities tools, the adaptive observer laws including Riccati equations, two differentiators, and many solvability conditions about the above Riccati equations are presented. Second, based on Lyapunov function approaches and the same inequalities tools, the proposed controllers are designed to guarantee the stability of the overall closed-loop systems, and many solvability conditions on the proposed controllers are analyzed too. More importantly, we give the structure of the common stable matrixes for this kind of control problem, including their disturbance structures and Lie algebra conditions. Finally, numerical simulations on the magnetic levitation systems show the effectiveness of our approaches.

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Acknowledgements

This work is Supported by National Key Research and Development Program of China (2017YFF0207400).

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Authors and Affiliations

  1. Key Laboratory of Complex System Intelligent Control and Decision, School of Automation, Beijing Institute of Technology, Beijing, China

    Shuli Guo

  2. Department of Cardiovascular Internal Medicine of Nanlou Branch, National Clinical Research Center for Geriatric Diseases, Chinese PLA General Hospital, Beijing, China

    Lina Han

Authors
  1. Shuli Guo
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  2. Lina Han
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Correspondence to Shuli Guo .

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Guo, S., Han, L. (2018). Fuzzy Observer, Fuzzy Controller Design, and Common Hurwitz Matrices for a Class of Uncertain Nonlinear Systems. In: Stability and Control of Nonlinear Time-varying Systems. Springer, Singapore. https://doi.org/10.1007/978-981-10-8908-4_5

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  • DOI: https://doi.org/10.1007/978-981-10-8908-4_5

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-8907-7

  • Online ISBN: 978-981-10-8908-4

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