Stability analysis for delayed quaternion-valued neural networks via nonlinear measure approach

In this paper, the existence and stability analysis of the quaternion-valued neural networks (QVNNs) with time delay are considered. Firstly, the QVNNs are equivalently transformed into four real-valued systems. Then, based on the Lyapunov theory, nonlinear measure approach, and inequality technique, some sufficient criteria are derived to ensure the existence and uniqueness of the equilibrium point as well as global stability of delayed QVNNs. In addition, the provided criteria are presented in the form of linear matrix inequality (LMI), which can be easily checked by LMI toolbox in MATLAB. Finally, two simulation examples are demonstrated to verify the effectiveness of obtained results. Moreover, the less conservatism of the obtained results is also showed by two comparison examples

Improved results on an extended dissipative analysis of neural networks with additive time-varying delays using auxiliary function-based integral inequalities

The issue of extended dissipative analysis for neural networks (NNs) with additive time-varying delays (ATVDs) is examined in this research. Some less conservative sufficient conditions are obtained to ensure the NNs are asymptotically stable and extended dissipative by building the agumented Lyapunov-Krasovskii functional, which is achieved by utilizing some mathematical techniques with improved integral inequalities like auxiliary function-based integral inequalities (gives a tighter upper bound). The present study aims to solve the $H_{\infty}, L_2-L_{\infty}$, passivity and $(Q, S, R)$-$\gamma$-dissipativity performance in a unified framework based on the extended dissipativity concept. Following this, the condition for the solvability of the designed NNs with ATVDs is presented in the form of linear matrix inequalities. Finally, the practicality and effectiveness of this approach were demonstrated through four numerical examples

Time-Varying Delay Passivity Analysis in 4 GHz Antennas Array Design

International audienceIn this paper, a new approach for synchronization of dynamical networks with time-delays is proposed. It is based on stability theory of coupled time-delayed dynamical systems. Some new criteria for stability analysis which ensure the synchronization of the networks are analytically derived. Conditions for synchronization,in the form of Linear Matrix Inequality, are established. They use the Lyapunov and Krasovskii stability theories. In this approach, parameter uncertainties are introduced in the network model. Numerical simulations show the efficiency of the proposed synchronization analysis. A network of 4-GHz smart antenna array is used and analyzed in some details. This array provides a control of the direction of the radiation pattern

Global rational stabilization of a class of nonlinear time-delay systems

The present paper is mainly aimed at introducing a novel notion of stability of nonlinear time-delay systems called Rational Stability. According to the Lyapunov-type, various sufficient conditions for rational stability are reached. Under delay dependent conditions, we suggest a nonlinear time-delay observer to estimate the system states, a state feedback controller and the observer-based controller rational stability is provided. Moreover, global rational stability using output feedback is given. Finally, the study presents simulation findings to show the feasibility of the suggested strategy

Global stability of Clifford-valued Takagi-Sugeno fuzzy neural networks with time-varying delays and impulses

summary:In this study, we consider the Takagi-Sugeno (T-S) fuzzy model to examine the global asymptotic stability of Clifford-valued neural networks with time-varying delays and impulses. In order to achieve the global asymptotic stability criteria, we design a general network model that includes quaternion-, complex-, and real-valued networks as special cases. First, we decompose the $n$-dimensional Clifford-valued neural network into $2^mn$-dimensional real-valued counterparts in order to solve the noncommutativity of Clifford numbers multiplication. Then, we prove the new global asymptotic stability criteria by constructing an appropriate Lyapunov-Krasovskii functionals (LKFs) and employing Jensen's integral inequality together with the reciprocal convex combination method. All the results are proven using linear matrix inequalities (LMIs). Finally, a numerical example is provided to show the effectiveness of the achieved results

Finite-time decentralized event-triggered feedback control for generalized neural networks with mixed interval time-varying delays and cyber-attacks

This article investigates the finite-time decentralized event-triggered feedback control problem for generalized neural networks (GNNs) with mixed interval time-varying delays and cyber-attacks. A decentralized event-triggered method reduces the network transmission load and decides whether sensor measurements should be sent out. The cyber-attacks that occur at random are described employing Bernoulli distributed variables. By the Lyapunov-Krasovskii stability theory, we apply an integral inequality with an exponential function to estimate the derivative of the Lyapunov-Krasovskii functionals (LKFs). We present new sufficient conditions in the form of linear matrix inequalities. The main objective of this research is to investigate the stochastic finite-time boundedness of GNNs with mixed interval time-varying delays and cyber-attacks by providing a decentralized event-triggered method and feedback controller. Finally, a numerical example is constructed to demonstrate the effectiveness and advantages of the provided control scheme

H ? filtering for stochastic singular fuzzy systems with time-varying delay

This paper considers the H? filtering problem for stochastic singular fuzzy systems with timevarying delay. We assume that the state and measurement are corrupted by stochastic uncertain exogenous disturbance and that the system dynamic is modeled by Ito-type stochastic differential equations. Based on an auxiliary vector and an integral inequality, a set of delay-dependent sufficient conditions is established, which ensures that the filtering error system is e?t - weighted integral input-to-state stable in mean (iISSiM). A fuzzy filter is designed such that the filtering error system is impulse-free, e?t -weighted iISSiM and the H? attenuation level from disturbance to estimation error is belowa prescribed scalar.Aset of sufficient conditions for the solvability of the H? filtering problem is obtained in terms of a new type of Lyapunov function and a set of linear matrix inequalities. Simulation examples are provided to illustrate the effectiveness of the proposed filtering approach developed in this paper

Synchronization of reaction–diffusion Hopfield neural networks with s-delays through sliding mode control

Synchronization of reaction–diffusion Hopfield neural networks with s-delays via sliding mode control (SMC) is investigated in this paper. To begin with, the system is studied in an abstract Hilbert space C([–r; 0];U) rather than usual Euclid space Rn. Then we prove that the state vector of the drive system synchronizes to that of the response system on the switching surface, which relies on equivalent control. Furthermore, we prove that switching surface is the sliding mode area under SMC. Moreover, SMC controller can also force with any initial state to reach the switching surface within finite time, and the approximating time estimate is given explicitly. These criteria are easy to check and have less restrictions, so they can provide solid theoretical guidance for practical design in the future. Three different novel Lyapunov–Krasovskii functionals are used in corresponding proofs. Meanwhile, some inequalities such as Young inequality, Cauchy inequality, Poincaré inequality, Hanalay inequality are applied in these proofs. Finally, an example is given to illustrate the availability of our theoretical result, and the simulation is also carried out based on Runge–Kutta–Chebyshev method through Matlab