Search

The extensively studied fractional-order dynamical networks only contain a uniform fractional derivative, which restricts the scope of fractional-order investigation. One type of Takagi–Sugeno fuzzy second-fractional-order linear networks is established in this article. First, by defining a novel Lyapunov functional, a sufficient criterion is offered to ensure global asymptotic stability of the addressed networks with time delay. Second, a fuzzy state-feedback control scheme is designed for the Takagi–Sugeno fuzzy second-fractional-order delayed linear networks to achieve global stabilization. Third, considering that only a few scholars have worked on adaptive control of fractional-order networks, an adaptive control method is also designed to realize the global stabilization of the Takagi–Sugeno fuzzy second-fractional-order linear networks, which does not contain the sign function and chattering problem can be averted. All results, given as algebraic criteria, are proved directly from the Takagi–Sugeno fuzzy second-fractional-order networks without utilizing the reduced-order approach. Three simulation examples are conducted to show the validity of the theoretical results at last. [ABSTRACT FROM AUTHOR]

The published stability criteria for impulsive neural networks are scale-free on time line, which is only appropriate for discrete or continuous ones. The issue of global exponential stability for impulsive delayed neural networks on time scales is analyzed by employing the convex combination method in this article. Several algebraic and linear matrix inequality conditions are proved by constructing impulse-dependent Lyapunov functionals and using timescale inequality techniques. Unlike the published works, impulsive control strategies can be designed by utilizing our theoretical results to stabilize delayed neural networks on time scales if they are unstable before introducing impulses. Sufficient criteria for global exponential stability in this article are derived based on the timescale theory, and they are applicable to discrete-time impulsive neural networks, their continuous-time analogues, and neural networks whose states are discrete at one time and continuous at another time. Four numerical examples are offered to demonstrate the effectiveness and superiority of our new theoretical results in the end. [ABSTRACT FROM AUTHOR]

Synchronization of a class of drive-response timescale-type nonautonomous proportional-delayed neural networks (TNPNNs) is addressed in this article. The key technique to cope with the proportional term is using comparison principle. By timescale theory, inequality technique, and comparison principle, criteria of synchronization are obtained. The method used in this article is effective to cope with TNPNNs and it is a direct approach as well by eliminating the conventional exponential transformation. The obtained results are verified with three examples. [ABSTRACT FROM AUTHOR]

This article concentrates on finite-time stabilization and energy consumption estimation for nonlinear systems with and without delay. By constructing an appropriate controller and utilizing inequality techniques, sufficient conditions are proposed to guarantee the finite-time stability of the delayed nonlinear system. Furthermore, the energy consumption produced in system controlling is estimated by inequality techniques. Then, we formulate similar results for the delay-free case. Finally, numerical examples are presented to demonstrate the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

This article deals with the asymptotic stability and synchronization of fractional-order neural networks (FONNs) with unbounded time-varying delays, in which FONNs can be the general nonlinear system. First, the existence of the equilibrium point of the nonlinear system is obtained, and the μ-type stability of fractional-order nonlinear systems is proved by the analytical method. Second, several sufficient conditions are derived to guarantee the μ-type stability of FONNs by taking easily implemented parameters. Moreover, the μ-type synchronization of drive-response systems is established by designing the linear controller. Especially, μ-type stability is the general stability, including Mittag-Leffler stability and power-stability, which is the extension of the Mittag-Leffler stability of FONNs. Finally, two numerical examples are presented to show the effectiveness of the results. [ABSTRACT FROM AUTHOR]

This paper investigates Cohen–Grossberg neural networks (CGNNs) with unbounded time-varying delays. The existence condition of multiple equilibrium points is established by the algebraic inequality method. And then, the ${\psi }$ -type stability is studied by analysis method for CGNNs with unbounded time-varying delays, and the relative convergence rate can be adjusted by the selection of ${\psi }$ -type functions. Moreover, by introducing the topological degree, the algebraic sum of the number of equilibria remains unchanged for any smooth function in the specified metric space. Finally, one numerical example is implemented to show the validity of the presented results. [ABSTRACT FROM AUTHOR]

This paper is concerned with multiple Lagrange stability under perturbation for recurrent neural networks with time-varying delays. This is different from traditional Lagrange stability, which means that multiple Lagrange stability under perturbation holds for any disturbance of initial value and any structural perturbation, within a specified and well-characterized set. In this paper, multiple Lagrange stability under perturbation with respect to a finite number of trivial solutions is established, which has good robustness. Under certain perturbation, the core of the proof of the boundedness of trajectories in mutually disjoint subregions is to employ the generalized differential inequality. The results supplement and extend some previous results, and they are applicable to robust analysis of multiple equilibria. Finally, numerical calculation and simulations are implemented to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the $\phi $ -type stability and robust stability for a general class of stochastic reaction–diffusion neural networks (SRDNNs) with Dirichlet boundary conditions, infinite discrete time-varying delays, and infinite continuously distributed delays. By virtue of inequality techniques, properties of $\boldsymbol M$ -matrix, and theories of stochastic analysis, several sufficient criteria are obtained to guarantee the almost sure $\boldsymbol \phi $ -type stability, $\boldsymbol p$ th moment $\boldsymbol \phi $ -type stability, and $\boldsymbol \phi $ -type robust stability of the underlying SRDNNs with hybrid unbounded time delays. With appropriate choices of the function $\boldsymbol \phi $ , the $\boldsymbol \phi $ -type stability reduces to the exponential stability, polynomial stability, and logarithmic stability. Additionally, the developed results herein include some existing ones as special cases. A numerical simulation is performed to substantiate the effectiveness and superiority of the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, coexistence and stability of multiple equilibrium points of fractional-order recurrent neural networks are addressed. Several sufficient conditions are derived for ascertaining the existence of \prod i=1^{n(2Ki+1)} equilibrium points ( Ki\geq 0 ) and the local Mittag–Leffler stability of \prod i=1^{n(Ki+1)} equilibrium points of them by using the geometrical properties of activation functions and algebraic properties of nonsingular M -matrix. In contrast with many existing results, the derived results cover both mono-stability and multistability, and the activation functions herein could be nonmonotonic and nonlinear in any open interval. In addition, three numerical examples are elaborated to substantiate the efficacy and characteristics of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper presents new theoretical results on the multistability analysis of a class of recurrent neural networks with nonmonotonic activation functions and mixed time delays. Several sufficient conditions are derived for ascertaining the existence of 3^n equilibrium points and the exponential stability of 2^n equilibrium points via state space partition by using the geometrical properties of activation functions and algebraic properties of nonsingular M -matrix. Compared with existing results, the conditions herein are much more computable with one order less linear matrix inequalities. Furthermore, the attraction basins of these exponentially stable equilibrium points are estimated. It is revealed that the attraction basins of the 2^n equilibrium points can be larger than their originally partitioned subspaces. Three numerical examples are elaborated with typical nonmonotonic activation functions to substantiate the efficacy and characteristics of the theoretical results. [ABSTRACT FROM PUBLISHER]