Global robust stability of time-delay systems with discontinuous activation functions under polytopic parameter uncertainties
Bull. Korean Math. Soc. 2010 Vol. 47, No. 1, 89-102
https://doi.org/10.4134/BKMS.2010.47.1.89
Printed January 1, 2010
Zengyun Wang, Lihong Huang, Yi Zuo, and Lingling Zhang
Hunan University, Hunan University, Changsha Univ. of Science and Technology, and Hunan University
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.
Keywords : global robust stability, delayed neural network, delay-independent condition, delay-dependent condition, linear matrix inequality, discontinuous neuron activation
MSC numbers : 93D09, 34D20, 34D23
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