Abstract
In this paper, the global asymptotical stability of Riemann-Liouville fractional-order neural networks with time-varying delays is studied. By combining the Lyapunov functional function and LMI approach, some sufficient criteria that guarantee the global asymptotical stability of such fractional-order neural networks with both discrete time-varying delay and distributed time-varying delay are derived. The stability criteria is suitable for application and easy to be verified by software. Lastly, some numerical examples are presented to check the validity of the obtained results.
Highlights
Fractional-order calculus has gained much attention in recent three decades because of its widespread application, such as engineering, diffusion equations, control science, biology, calorifics, and so on [1,2,3,4,5]
As an important branch of fractional-order calculus, stability has been studied by many scholars [6,7,8,9,10,11,12,13,14,15]
In [19,20], the asymptotical stability of fractional systems has been analyzed by using Lyapunov functional method
Summary
Fractional-order calculus has gained much attention in recent three decades because of its widespread application, such as engineering, diffusion equations, control science, biology, calorifics, and so on [1,2,3,4,5]. Mathematics 2019, 7, 138 this thesis consider the global asymptotical stability of Riemann-Liouville fractional neural networks with time-varying delays as follows:. A = diag( a1 , a2 , · · · , an ) is a positive diagonal matrix; B, C, D ∈ Rn×n stand for constant connection weights matrices; I ∈ Rn denotes an input of neuron; fe(ψ) = [ fe (ψ1 ), fe (ψ2 ), · · · , fen (ψn )] T , ge(ψ) = [ ge (ψ1 ), ge (ψ2 ), · · · , gen (ψn )] T , e h ( ψ ) = [e h1 (ψ1 ), e h2 (ψ2 ), · · · , e hn (ψn )] T are activation functions e e with f (0) = h(0) = ge(0) = 0 and δ(t) is smooth time-varying delay which follows.
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