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Delay decomposition approach to state estimation of neural networks with mixed time-varying delays and Markovian jumping parameters. (English) Zbl 1271.34083

This paper examines the mean-square stability of the error between neural networks with mixed time-varying delays and Markovian switching of the form

x ˙(t)=-A(r(t))x(t)+B(r(t))g(x(t))+B 1 (r(t))g(x(t-τ(t)))++E(r(t)) t-σ(t) t g(x(s))ds+J(r(t)),

and its full-order state estimation of the form

x ^ ˙(t)=-A(r(t))x ^(t)+B(r(t))g(x ^(t))+B 1 (r(t))g(x ^(t-τ(t)))+E(r(t)) t-σ(t) t g(x ^(s))ds+J(r(t))+K(r(t))(y-y ^),
y ^(t)=c(r(t))x ^(t)+D(r(t))f(t,x ^(t))·

The main tools are Lyapunov-Krasovskii functionals and the LMI approach. This paper includes some useful inequalities.

Reviewer: Fuke Wu (Wuhan)
34K50Stochastic functional-differential equations
92B20General theory of neural networks (mathematical biology)
34K35Functional-differential equations connected with control problems