Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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GLOBAL ROBUST STABILITY OF TIME-DELAY SYSTEMS WITH DISCONTINUOUS ACTIVATION FUNCTIONS UNDER POLYTOPIC PARAMETER UNCERTAINTIES

  • Wang, Zengyun (College of Mathematics and Economtrics, Hunan University) ;
  • Huang, Lihong (College of Mathematics and Economtrics, Hunan University) ;
  • Zuo, Yi (School of Energy and Power Engineering, Changsha University of Science and Technology, Department of Applied Mathematics, University of Waterloo) ;
  • Zhang, Lingling (College of Mathematics and Economtrics, Hunan University)
  • Published : 2010.01.31
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Abstract

This paper concerns the problem of global robust stability of a time-delay discontinuous system with a positive-defined connection matrix under polytopic-type uncertainty. In order to give the stability condition, we firstly address the existence of solution and equilibrium point based on the properties of M-matrix, Lyapunov-like approach and the theories of differential equations with discontinuous right-hand side as introduced by Filippov. Second, we give the delay-independent and delay-dependent stability condition in terms of linear matrix inequalities (LMIs), and based on Lyapunov function and the properties of the convex sets. One numerical example demonstrate the validity of the proposed criteria.

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