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\(H_\infty \) Sliding Mode Observer Design for Nonlinear Time Delay Systems

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Nonlinear Stochastic Systems with Network-Induced Phenomena

Abstract

In this chapter, we investigate the \(H_\infty \) sliding mode observer (SMO) design problem for a class of discrete time delay nonlinear systems. The nonlinear descriptions quantify the maximum possible derivations from a linear model, and the system states are allowed to be immeasurable. A discrete-time discontinuous switched term is firstly proposed to make sure that the reaching condition holds. Then, by constructing a new Lyapunov–Krasovskii functional based on the idea of delay fractioning and introducing some appropriate free-weighting matrices, a sufficient condition is established to guarantee the desired performance of the error dynamics in the specified sliding mode surface by solving a minimization problem. This minimization problem involves linear objective and linear matrix inequalities that can be easily tested by means of standard numerical software.

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Authors and Affiliations

  1. Department of Applied Mathematics, Harbin University of Science and Technology, Harbin, China

    Jun Hu

  2. Department of Information Systems and Computing, Brunel University, Uxbridge, Middlesex, UK

    Zidong Wang

  3. Research Institute of Intelligent Control and Systems, Harbin Institute of Technology, Harbin, China

    Huijun Gao

Authors
  1. Jun Hu
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  2. Zidong Wang
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  3. Huijun Gao
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Correspondence to Jun Hu .

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Hu, J., Wang, Z., Gao, H. (2015). \(H_\infty \) Sliding Mode Observer Design for Nonlinear Time Delay Systems. In: Nonlinear Stochastic Systems with Network-Induced Phenomena. Springer, Cham. https://doi.org/10.1007/978-3-319-08711-5_5

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  • DOI: https://doi.org/10.1007/978-3-319-08711-5_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08710-8

  • Online ISBN: 978-3-319-08711-5

  • eBook Packages: EngineeringEngineering (R0)

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