An LMI Approach for Stability Analysis and Output-Feedback Stabilization of Discrete-Time Lur’e Systems Using Zames-Falb Multipliers - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles IEEE Control Systems Letters Year : 2021

An LMI Approach for Stability Analysis and Output-Feedback Stabilization of Discrete-Time Lur’e Systems Using Zames-Falb Multipliers

Abstract

This paper investigates the problem of stability analysis and output-feedback stabilization of discrete-time Lur'e systems where the nonlinearity is odd and slope bounded. Using the linear matrix inequality (LMI) conditions from the literature to handle the 1 norm and positive realness constraints, an iterative algorithm based on LMIs is constructed to assess stability through the existence of a Zames-Falb multiplier of any given order based on independent positive definite matrices for the 1 norm and positive realness. More important, the method can also deal with output-feedback stabilization. Numerical examples illustrate the performance of the proposed approach when compared with other methods.

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Dates and versions

hal-03485392 , version 1 (17-12-2021)

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Ariádne L J Bertolin, Ricardo C L F Oliveira, Giorgio Valmorbida, Pedro L D Peres. An LMI Approach for Stability Analysis and Output-Feedback Stabilization of Discrete-Time Lur’e Systems Using Zames-Falb Multipliers. IEEE Control Systems Letters, 2021, 6, pp.710-715. ⟨10.1109/LCSYS.2021.3086427⟩. ⟨hal-03485392⟩
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