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Generalized \(H_2\) Sliding Mode Control for a Class of (TS) Fuzzy Descriptor Systems with Time-Varying Delay and Nonlinear Perturbations

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Advances and Applications in Sliding Mode Control systems

Part of the book series: Studies in Computational Intelligence ((SCI,volume 576))

Abstract

This chapter considers the development of robust performance control based-on integral sliding-mode for descriptor system with nonlinearities and perturbations which consist on external disturbances and model uncertainties of great possibility time-varying manner. Sliding-mode control (SMC) is one of robust control methodologies that deal with both linear and nonlinear systems. The most distinguishing feature of (SMC) is its robustness as well as in the case of invariant control systems. Loosely speaking, the term “invariant” means that the system is completely insensitive to parametric uncertainty and external disturbances. Another type of advanced sliding mode control law is “integral sliding mode”. The integral sliding mode control differs from the sliding mode control by the use of an integration term in the sliding variable (surface) design in addition to the linear term. In this work the problem of sliding mode control (SMC) for a class of uncertain (TS) fuzzy descriptor systems with time-varying delay is studied. An integral-type sliding function is proposed and a delay-dependent criterion is developed in terms of linear matrix inequality (LMI), which ensures the sliding mode dynamics to be robustly admissible with generalized \(H_2\) disturbance rejection level. Moreover, a SMC law is established to satisfy the reaching condition of the specified sliding surface for all admissible uncertainties and time-varying delay. The developed results are tested on two representative examples to illustrate the theoretical developments.

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Authors and Affiliations

  1. Laboratory of Sciences and Techniques of Automatic Control and Computer Engineering (Lab-STA), Sfax, Tunisia

    Mourad Kchaou & Ahmed Toumi

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  1. Mourad Kchaou
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  2. Ahmed Toumi
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Correspondence to Mourad Kchaou .

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Editors and Affiliations

  1. Faculty of Computers and Information, Benha University, Benha, Egypt

    Ahmad Taher Azar

  2. Department of Engineering Design and Mathematics, University of the West of England, Bristol, United Kingdom

    Quanmin Zhu

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Kchaou, M., Toumi, A. (2015). Generalized \(H_2\) Sliding Mode Control for a Class of (TS) Fuzzy Descriptor Systems with Time-Varying Delay and Nonlinear Perturbations. In: Azar, A., Zhu, Q. (eds) Advances and Applications in Sliding Mode Control systems. Studies in Computational Intelligence, vol 576. Springer, Cham. https://doi.org/10.1007/978-3-319-11173-5_13

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  • DOI: https://doi.org/10.1007/978-3-319-11173-5_13

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  • Print ISBN: 978-3-319-11172-8

  • Online ISBN: 978-3-319-11173-5

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