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Towards Enhancing Nonlinear Observers for Lipschitz System: Exploiting the Matrix Multipliers-based LMIs
  • Shivaraj Mohite,
  • Marouane Alma,
  • Ali Zemouche
Shivaraj Mohite
Universite de Lorraine

Corresponding Author:shivaraj.mohite@univ-lorraine.fr

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Marouane Alma
Universite de Lorraine
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Ali Zemouche
Universite de Lorraine
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Abstract

This article is focused on the design of an LMI-based observer for the class of disturbance-affected nonlinear systems. Two novel LMI conditions are derived by deploying a more general form of the matrix multiplier compared to the one used in the literature. The first method is based on the use of the H ∞ criterion, while the second one utilises an ISS notion. Both LMIs are developed by employing the reformulated Lipschitz property, a well-known LPV approach and the new variant of Young inequality. The key element of the proposed LMI conditions is the incorporation of the novel matrix multipliers which allow us to include some additional decision variables as compared to the methods proposed in the literature. These additional variables add extra degrees of freedom, thus enhancing the LMI feasibility. Furthermore, the effectiveness of the proposed methodologies is showcased through a numerical example.
Submitted to International Journal of Robust and Nonlinear Control
18 Jun 20241st Revision Received
20 Jun 2024Reviewer(s) Assigned
10 Jul 2024Review(s) Completed, Editorial Evaluation Pending
11 Jul 2024Editorial Decision: Accept