A new upper bound for the norm of interval matrices with application to robust stability analysis of delayed neural networks
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The main problem with the analysis of robust stability of neural networks is to find the upper bound norm for the intervalized interconnection matrices of neural networks. In the previous literature, the major three upper bound norms for the intervalized interconnection matrices have been reported and they have been successfully applied to derive new sufficient conditions for robust stability of delayed neural networks. One of the main contributions of this paper will be the derivation of a new upper bound for the norm of the intervalized interconnection matrices of neural networks. Then, by exploiting this new upper bound norm of interval matrices and using stability theory of Lyapunov functionals and the theory of homomorphic mapping, we will obtain new sufficient conditions for the existence, uniqueness and global asymptotic stability of the equilibrium point for the class of neural networks with discrete time delays under parameter uncertainties and with respect to continuous and slope-bounded activation functions. The results obtained in this paper will be shown to be new and they can be considered alternative results to previously published corresponding results. We also give some illustrative and comparative numerical examples to demonstrate the effectiveness and applicability of the proposed robust stability condition.
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New Criteria for Global Robust Stability of Delayed Neural Networks With Norm-Bounded Uncertainties Arık, Sabri (IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2014-06)In this paper, we study the global asymptotic robust stability of delayed neural networks with norm-bounded uncertainties. By employing the Lyapunov stability theory and homeomorphic mapping theorem, we derive some new ...
Arık, Sabri (Elsevier Science BV, 2014-03-27)This paper is concerned with the global asymptotic stability problem of dynamical neural networks with multiple time delays under parameter uncertainties. First carrying out an analysis of existence and uniqueness of the ...
Arık, Sabri (PERGAMON-ELSEVIER SCIENCE LTD., 2014-06)This paper proposes a new alternative sufficient condition for the existence, uniqueness and global asymptotic stability of the equilibrium point for the class of delayed neural networks under the parameter uncertainties ...