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Stabilisation of neutral systems with saturating control inputs

Author

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  • J.M. da Silva
  • A. Seuret
  • E. Fridman
  • J.P. Richard

Abstract

This article focuses on the stabilisation problem of neutral systems in the presence of time-varying delays and control saturation. Based on a descriptor approach and the use of a modified sector relation, global and local stabilisation conditions are derived using Lyapunov–Krasovskii functionals. These conditions, formulated directly as linear matrix inequalities (LMIs), allow one to relate the control law to be computed to a set of admissible initial conditions, for which the asymptotic and exponential stabilities of the closed-loop system are ensured. An extension of these conditions to the particular case of retarded systems is also provided. From the theoretical conditions, optimisation problems with LMI constraints are therefore proposed to compute stabilising state feedback gains with the aim of ensuring stability for a given set of admissible initial conditions or the global stability of the closed-loop system. A numerical example illustrates the application of the proposed results.

Suggested Citation

  • J.M. da Silva & A. Seuret & E. Fridman & J.P. Richard, 2011. "Stabilisation of neutral systems with saturating control inputs," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(7), pages 1093-1103.
    • Handle: RePEc:taf:tsysxx:v:42:y:2011:i:7:p:1093-1103
    DOI: 10.1080/00207720903353575
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    Cited by:

    1. Gongfei Song & Jianzhen Li & Ze Li & Yuming Bo, 2015. "Quantised feedback control for bilinear systems with actuator saturation," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(8), pages 1380-1391, June.
    2. Wu, Hongjuan & Li, Chuandong & He, Zhilong & Wang, Yinuo & He, Yingying, 2021. "Lag synchronization of nonlinear dynamical systems via asymmetric saturated impulsive control," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).

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