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Robust stability and stabilization of fractional-order linear systems with nonlinear uncertain parameters: An LMI approach

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  • Xing, Sheng Yan
  • Lu, Jun Guo

Abstract

This paper investigates the stability and stabilization problem of fractional-order linear systems with nonlinear uncertain parameters, which allow second-order uncertain parameters. The uncertainty in the fractional-order model appears in the form of a combination of additive uncertainty and multiplicative uncertainty. It is shown that the fractional-order model has a strong practical background. Sufficient conditions for the stability and stabilization of such fractional-order model are presented in terms of linear matrix inequalities. Two examples are given to show the effectiveness of the proposed results.

Suggested Citation

  • Xing, Sheng Yan & Lu, Jun Guo, 2009. "Robust stability and stabilization of fractional-order linear systems with nonlinear uncertain parameters: An LMI approach," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1163-1169.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:2:p:1163-1169
    DOI: 10.1016/j.chaos.2009.03.017
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    1. Lokenath Debnath, 2003. "Recent applications of fractional calculus to science and engineering," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-30, January.
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    1. Hong Li & Jun Cheng & Hou-Biao Li & Shou-Ming Zhong, 2019. "Stability Analysis of a Fractional-Order Linear System Described by the Caputo–Fabrizio Derivative," Mathematics, MDPI, vol. 7(2), pages 1-9, February.
    2. Fiuzy, Mohammad & Shamaghdari, Saeed, 2023. "Robust H∞-PID control Stability of fractional-order linear systems with Polytopic and two-norm bounded uncertainties subject to input saturation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 550-581.
    3. Chen, Liping & Wu, Ranchao & He, Yigang & Yin, Lisheng, 2015. "Robust stability and stabilization of fractional-order linear systems with polytopic uncertainties," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 274-284.

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