New Results on Stability and Stabilization of Delayed Caputo Fractional Order Systems with Convex Polytopic Uncertainties

Abstract

In this paper, the problems of robust stability and stabilization, for the first time, are studied for delayed fractional-order linear systems with convex polytopic uncertainties. The authors derive some sufficient conditions for the problems based on linear matrix inequality technique combined with fractional Razumikhin stability theorem. All the results are obtained in terms of linear matrix inequalities that are numerically tractable. The proposed results are quite general and improve those given in the literature since many factors, such as discrete and distributed delays, convex polytopic uncertainties, global stability and stabilizability, are considered. Numerical examples and simulation results are given to illustrate the effectiveness of the effectiveness of our results.

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Correspondence to Cong Huong Dinh or Viet Thuan Mai.

Additional information

The research of Mai Viet Thuan is was supported by Ministry of Education and Training of Vietnam (B2020-TNA).

This paper was recommended for publication by Editor SUN Jian.

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Dinh, C.H., Mai, V.T. & Duong, T.H. New Results on Stability and Stabilization of Delayed Caputo Fractional Order Systems with Convex Polytopic Uncertainties. J Syst Sci Complex 33, 563–583 (2020). https://doi.org/10.1007/s11424-020-8338-2

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Keywords

  • Convex polytopic uncertainty
  • delayed caputo fractional-order systems
  • fractional Razumikhin theorem
  • linear matrix inequality
  • robust stability
  • robust stabilization