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LMI-based robust tracking of a class of MIMO nonlinear systems

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Abstract

Reference tracking problem for MIMO Lipschitz nonlinear systems is examined here. Presently a vast literature exists on observer design of unforced systems containing Lipschitz nonlinearities. However, these existing results cannot be readily extended for controller design containing reference tracking ability. Here a Linear State Variable Feedback (LSVF) controller is designed for MIMO Lipschitz nonlinear systems with norm-bounded parametric uncertainties using the concept of input to state stability Lyapunov functions. The whole problem is cast into a framework of Linear Matrix Inequalities, to exploit its numerical capabilities. Analytical proofs are supplemented with simulation examples, which show certain advantages over existing results. Apart from state feedback, observer-based output feedback is also considered for controller design.

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Acknowledgements

This work is financially supported by the Indian Institute of Engineering Science and Technology, Shibpur, West Bengal, India.

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Authors and Affiliations

  1. Department of Electrical Engineering, Indian Institute of Engineering Sciences and Technology, Shibpur, Howrah, 711103, India

    Arunima Mukherjee & Aparajita Sengupta

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  1. Arunima Mukherjee
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  2. Aparajita Sengupta
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Correspondence to Arunima Mukherjee.

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Mukherjee, A., Sengupta, A. LMI-based robust tracking of a class of MIMO nonlinear systems. Sādhanā 44, 199 (2019). https://doi.org/10.1007/s12046-019-1182-1

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