Energy-to-peak synchronization for uncertain reaction-diffusion delayed neural networks

Abstract

This paper is devoted to energy-to-peak synchronization for uncertain reaction-diffusion delayed neural networks subject to external disturbances. The purpose is to determine a controller in such a way that the drive-response systems not only achieve asymptotical synchronization in the absence of disturbances but also possess a predefined energy-to-peak disturbance-rejection level under zero initial conditions. Through the use of Lyapunov-Krasovskii functionals and various integral inequalities, both delay-independent and dependent conditions are proposed in the form of linear matrix inequalities. When these conditions hold, the needed controller gains can be calculated directly. A numerical example is provided to show the applicability and reduced conservativeness of the present results.

Weight learning for ℋ∞$$ {\mathscr{H}}_{\infty } $$ stabilization of uncertain switched neural networks with external disturbance and reaction‐diffusion

“…Consider the following neural network model: (s, t)) = [𝜙 1 (𝜈(s, t)), … , 𝜙 n (𝜈(s, t))] T ∶ R n → R n represents the activation function vector which satisfies 𝜙(0) = 0 and the common Lipschitz condition subject to Lipschitz constant L 𝜙 > 0. 33,34 The initial and boundary conditions are given as…”

Mean-square asymptotic synchronization of complex dynamical networks subject to communication delay and switching topology

“…The coupling strength of the system is denoted by a constant c; σ(t) denotes the continuous time-variant delay that satisfies 0 σ 1 σ(t) σ 2 , σ 12 = σ 2 − σ 1 , where σ 1 and σ 2 are constants that correspond to the lower and upper bounds of σ(t), respectively. Note that we do not impose differentiability constraints on the time delay function as in [21][22][23][24].…”