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Lyapunov Functional Approach to Stability Analysis of Riemann‐Liouville Fractional Neural Networks with Time‐Varying Delays
Author(s) -
Zhang Hai,
Ye Renyu,
Cao Jinde,
Ahmed Alsaedi,
Li Xiaodi,
Wan Ying
Publication year - 2018
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.1675
Subject(s) - mathematics , fractional calculus , nonlinear system , artificial neural network , exponential stability , lyapunov function , stability (learning theory) , control theory (sociology) , derivative (finance) , mathematical analysis , computer science , physics , control (management) , quantum mechanics , machine learning , artificial intelligence , financial economics , economics
This paper is concerned with the globally asymptotic stability of the Riemann‐Liouville fractional‐order neural networks with time‐varying delays. The Lyapunov functional approach to stability analysis for nonlinear fractional‐order functional differential equations is discussed. By constructing an appropriate Lyapunov functional associated with the Riemann‐Liouville fractional integral and derivative, the asymptotic stability criteria of fractional‐order neural networks with time‐varying delays and constant delays are derived. The advantage of our proposed method is that one may directly calculate the first‐order derivative of the Lyapunov functional. Two numerical examples are also presented to illustrate the validity and feasibility of the theoretical results. With the increasing of the order of fractional derivatives, the state trajectories of neural networks show that the speeds of converging toward zero solution are faster and faster.