Finite-time passivity for neutral-type neural networks with time-varying delays – via auxiliary function-based integral inequalities

In this paper, we investigated the problem of the finite-time boundedness and finitetime passivity for neural networks with time-varying delays. A triple, quadrable and five integral terms with the delay information are introduced in the new Lyapunov–Krasovskii functional (LKF). Based on the auxiliary integral inequality, Writinger integral inequality and Jensen’s inequality, several sufficient conditions are derived. Finally, numerical examples are provided to verify the effectiveness of the proposed criterion. There results are compared with the existing results.&nbsp

STABILITY, FINITE-TIME STABILITY AND PASSIVITY CRITERIA FOR DISCRETE-TIME DELAYED NEURAL NETWORKS

In this paper, we present the problem of stability, finite-time stability and passivity for discrete-time neural networks (DNNs) with variable delays. For the purposes of stability analysis, an augmented Lyapunov-Krasovskii functional (LKF) with single and double summation terms and several augmented vectors is proposed by decomposing the time-delay interval into two non-equidistant subintervals. Then, by using the Wirtinger-based inequality, reciprocally and extended reciprocally convex combination lemmas, tight estimations for sum terms in the forward difference of LKF are given. In order to relax the existing results, several zero equalities are introduced and stability criteria are proposed in terms of linear matrix inequalities (LMIs). The main objective for the finite-time stability and passivity analysis is how to effectively evaluate the finite-time passivity conditions for DNNs. To achieve this, some weighted summation inequalities are proposed for application to a finite-sum term appearing in the forward difference of LKF, which helps to ensure that the considered delayed DNN is passive. The derived passivity criteria are presented in terms of linear matrix inequalities. Some numerical examples are presented to illustrate the proposed methodology

Nonlinear Systems

Open Mathematics is a challenging notion for theoretical modeling, technical analysis, and numerical simulation in physics and mathematics, as well as in many other fields, as highly correlated nonlinear phenomena, evolving over a large range of time scales and length scales, control the underlying systems and processes in their spatiotemporal evolution. Indeed, available data, be they physical, biological, or financial, and technologically complex systems and stochastic systems, such as mechanical or electronic devices, can be managed from the same conceptual approach, both analytically and through computer simulation, using effective nonlinear dynamics methods. The aim of this Special Issue is to highlight papers that show the dynamics, control, optimization and applications of nonlinear systems. This has recently become an increasingly popular subject, with impressive growth concerning applications in engineering, economics, biology, and medicine, and can be considered a veritable contribution to the literature. Original papers relating to the objective presented above are especially welcome subjects. Potential topics include, but are not limited to: Stability analysis of discrete and continuous dynamical systems; Nonlinear dynamics in biological complex systems; Stability and stabilization of stochastic systems; Mathematical models in statistics and probability; Synchronization of oscillators and chaotic systems; Optimization methods of complex systems; Reliability modeling and system optimization; Computation and control over networked systems

Event-triggered communication for passivity and synchronisation of multi-weighted coupled neural networks with and without parameter uncertainties

A multi-weighted coupled neural networks (MWCNNs) model with event-triggered communication is studied here. On the one hand, the passivity of the presented network model is studied by utilising Lyapunov stability theory and some inequality techniques, and a synchronisation criterion based on the obtained output-strict passivity condition of MWCNNs with eventtriggered communication is derived. On the other hand, some robust passivity and robust synchronisation criteria based on output-strict passivity of the proposed network with uncertain parameters are presented. At last, two numerical examples are provided to testify the effectiveness of the output-strict passivity and robust synchronisation results

Robust passivity of coupled Cohen-Grossberg neural networks with reaction-diffusion terms

In this paper, we deal with the robust passivity problem for coupled reaction-diffusion Cohen-Grossberg neural networks (CRDCGNNs) with spatial diffusion coupling and state coupling. First, we present the network model for CRDCGNNs with state coupling and establish some robust passivity conditions for this kind of CRDCGNNs. Then, the investigation on robust passivity for CRDCGNNs with spatial diffusion coupling is carried out similarly. At last, the feasibility of the obtained theoretical results is demonstrated by one example with simulation results

New results on finite-/fixed-time synchronization of delayed memristive neural networks with diffusion effects

In this paper, we further investigate the finite-/fixed-time synchronization (FFTS) problem for a class of delayed memristive reaction-diffusion neural networks (MRDNNs). By utilizing the state-feedback control techniques, and constructing a general Lyapunov functional, with the help of inequality techniques and the finite-time stability theory, novel criteria are established to realize the FFTS of the considered delayed MRDNNs, which generalize and complement previously known results. Finally, a numerical example is provided to support the obtained theoretical results

New Stability Criterion for Discrete-Time Genetic Regulatory Networks with Time-Varying Delays and Stochastic Disturbances

We propose an improved stability condition for a class of discrete-time genetic regulatory networks (GRNs) with interval time-varying delays and stochastic disturbances. By choosing an augmented novel Lyapunov-Krasovskii functional which contains some triple summation terms, a less conservative sufficient condition is obtained in terms of linear matrix inequalities (LMIs) by using the combination of the lower bound lemma, the discrete-time Jensen inequality, and the free-weighting matrix method. It is shown that the proposed results can be readily solved by using the Matlab software. Finally, two numerical examples are provided to illustrate the effectiveness and advantages of the theoretical results