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Improved LMI Conditions for Unknown Input Observer Design of Discrete-time LPV Systems

Abstract

This paper presents a novel unknown input observer (UIO) design for discrete-time linear parameter-varying (LPV) systems. One feature of the proposed approach is the ability of handling LPV systems with variation in both states and outputs matrices. The design problem has been formulated using a less conservative discrete-time stability condition which allows to obtain proportional UIO and proportional-integral UIO structures. Existence conditions for both structures are provided. These poly-quadratic conditions rely on the use of parameter-dependent Lyapunov functions defined in terms of Linear Matrix Inequalities. Furthermore, an extended formulation using the performance index is also derived. Finally, the effectiveness of the proposed design method is illustrated through numerical examples.

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Correspondence to Matheus Senna de Oliveira.

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Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Recommended by Associate Editor Nam H. Jo under the direction of Editor Jessie (Ju H.) Park. This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior — Brasil (CAPES) — Finance Code 001.

Matheus Senna de Oliveira received his B.Eng. degree in Control and Automation and an M.S in Electrical Engineering from the Pontifical Catholic University of Rio Grande do Sul, in 2015 and 2018, respectively. He is currently working toward a Ph.D. degree in Electronic Engineering at the Instituto Tecnológico de Aeronáutica. His main research interests are robust control, LPV systems, performance criteria and LMIs.

Renan Lima Pereira received his B.Sc. degree in electrical engineering from Federal University of Maranhäo in 2009, and his M.Sc and Ph.D. degrees in electronic engineering from Instituto Tecnológico de Aeronáutica, in 2011 and 2014, respectively, where he has been a professor since 2018. His research interests include robust control, gain-scheduled control and optimization.

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de Oliveira, M.S., Pereira, R.L. Improved LMI Conditions for Unknown Input Observer Design of Discrete-time LPV Systems. Int. J. Control Autom. Syst. 18, 2543–2551 (2020). https://doi.org/10.1007/s12555-019-0407-8

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Keywords

  • Discrete-time LPV systems
  • linear matrix inequalities
  • poly-quadratic conditions
  • unknown input observers