Extended dissipativity state estimation for generalized neural networks with time-varying delay via delay-product-type functionals and integral inequality

Dissipativity analysis for Lur'e systems with two additive time‐varying delays via some novel Lyapunov–Krasovskii functionals

“…Dissipative criteria of various delayed systems were presented in many existing literatures 37‐41 . For example, the dissipativity of Lur'e distributed parameter control systems, 42 the finite‐time extended dissipativity of the interval type‐2 fuzzy systems with probabilistic time‐varying delay, 43 the robust dissipativity of neural networks with both time‐varying delay and randomly occurring uncertainties, 44 the extended dissipativity state estimation for delayed generalized neural networks 45 . The problem of strictly $$$ \left(Q,S,R\right)-\gamma $$$ dissipativity analysis of neural networks with ATDs was studied in Reference 46, the values of $$$ \gamma $$$ were given by the proposed strictly $$$ \left(Q,S,R\right)-\gamma $$$ dissipativity sufficient conditions.…”

“…[37][38][39][40][41] For example, the dissipativity of Lur'e distributed parameter control systems, 42 the finite-time extended dissipativity of the interval type-2 fuzzy systems with probabilistic time-varying delay, 43 the robust dissipativity of neural networks with both time-varying delay and randomly occurring uncertainties, 44 the extended dissipativity state estimation for delayed generalized neural networks. 45 The problem of strictly (Q, S, R) − 𝛾 dissipativity analysis of neural networks with ATDs was studied in Reference 46, the values of 𝛾 were given by the proposed strictly (Q, S, R) − 𝛾 dissipativity sufficient conditions. It is worth noting that most existing literature restricted all of the Lyapunov matrices were requested positive definite, which makes it possible to further improve the dissipativity and stability criteria of delayed systems in the case of partly Lyapunov matrices being nonpositive definite.…”

State Estimation for Standard Neural Network Models with Time‐Varying Delays

“…erefore, it is essential to estimate the neuron state through the available output measurements. Recently, the delay-dependent state estimation problem for neural networks has received much significant achievements [29][30][31][32][33][34][35][36][37]. In [29], delay-dependent state estimation criteria were obtained by employing free matrix-based integral inequality.…”

“…e criteria were given to guarantee error system is asymptotically stable; meanwhile, the estimator gain and L 2 -L ∞ performance index have been obtained. e extended dissipative state estimation issue was investigated in [32][33][34].…”

“…e system considered is generalized neural networks in [32,33]. In [34], the existences of the estimator gain matrices for static neural networks were investigated by constructing a new delay-product-type functional.…”