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Observer-Based \(H_\infty \) Control for One-Sided Lipschitz Nonlinear Systems with Uncertain Input Matrix

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Abstract

This paper investigates the problem of observer-based \(H_\infty \) control for one-sided Lipschitz nonlinear systems subject to parametric uncertainties and external disturbances. In order to relax some conservatisms and limitations of the traditional Lipschitz condition, the one-sided Lipschitz and quadratically inner-bounded conditions are used. On the contrary to the methods proposed in the literature, our method allows for uncertainty in the input matrix B, as well as the dynamic and output matrices A and C. To derive design conditions in terms of LMIs, the well-known Young’s relation is employed for handling the bilinear terms naturally arising in observer-based controller design. Finally, two examples are presented to demonstrate the validity of the theoretical results.

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Data Availability Statement

The datasets generated during the current study are available from the corresponding author on reasonable request.

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Authors and Affiliations

  1. Faculty of Electrical and Computer Engineering, Babol Noshirvani University of Technology, Babol, Iran

    Majid Shahbazzadeh & Seyed Jalil Sadati

  2. Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran

    Homa Salehifar

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  1. Homa Salehifar
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  2. Majid Shahbazzadeh
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Salehifar, H., Shahbazzadeh, M. & Sadati, S.J. Observer-Based \(H_\infty \) Control for One-Sided Lipschitz Nonlinear Systems with Uncertain Input Matrix. Circuits Syst Signal Process 41, 1406–1425 (2022). https://doi.org/10.1007/s00034-021-01847-x

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