This paper focuses on the problem of delay- dependent stability analysis of neural networks with variable delay. Two types of variable delay are considered: one is differentiable and has bounded derivative; the other one is continuous and may vary very fast. By introducing a new type of Lyapunov-Krasovskii functional, new delay-dependent sufficient conditions for exponential stability of delayed neural networks are derived in terms of linear matrix inequalities. We also obtain delay-independent stability criteria. These criteria can be tested numerically and very efficiently using interior point algorithms. Two examples are presented which show our results are less conservative than the existing stability criteria.

An LMI approach to exponential stability analysis of neural networks with time-varying delay

New studies on dynamic analysis of inertial neural networks involving non-reduced order method

Some new results on stability and synchronization for delayed inertial neural networks based on non-reduced order method

Global exponential stability in Lagrange sense for inertial neural networks with time-varying delays

This paper is concerned with the problem of synchronization for inertial neural networks (INNs) with heterogeneous time-varying delays (HTVDs) through quantized sampled-data control. The control scheme, which takes the communication limitations of quantization and variable sampling into account, is first employed for tackling the synchronization of INNs. A novel Lyapunov–Krasovskii functional (LKF) is constructed for synchronizing an error system. Compared with existing LKFs by the largest upper bound of all HTVDs, the proposed LKF is superior, since it can make full use of the information on the lower and upper bounds of each HTVD. Based on the LKF and a new integral inequality technique, less conservative synchronization criteria are derived. The desired quantized sampled-data controller is designed by solving a set of linear matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness and conservatism reduction of the proposed results.

Quantized Sampled-Data Control for Synchronization of Inertial Neural Networks With Heterogeneous Time-Varying Delays

Global Lagrange stability for inertial neural networks with mixed time-varying delays

Stability of real time hybrid simulation (RTHS) has attracted considerable attention since actuator delay would deviate experiment results or even destabilize the real‐time test. Previous studies have extensively investigated stability of RTHS for linear systems, while stability of RTHS for nonlinear system remains unclear. This study introduces the Takagi‐Sugeno (T‐S) method to describe the nonlinear behavior in a piecewise linear way, then investigates the stability of nonlinear system with time delay through the Lyapunov‐Krasovskii (L‐K) theory. Such approach successfully solves the stability problem of RTHS with coupled bilinear‐hysteresis substructure and actuator delay, and proposes a stability criterion in the form of linear matrix inequality (LMI). It proves that the stability of RTHS is determined by the most unfavorable state of nonlinear system. In the SDOF case with stiffness softening, the initial elastic state is the most unfavorable; while for the MDOF case with multiple delays, the stability is determined by the overlap part of stable region of each nonlinear state. The computational simulation and experimental results show that the difference between linear‐ and nonlinear hysteretic system with time delay is that when instability occurs, latter could remain energy balanced since the time‐delay energy is dissipated by hysteresis behavior, while energy accumulates in the former leading to unbounded responses. The proposed approach provides a potential tool for experimental design of RTHS before the test, the time‐delay control during the test and error evaluation after the test.

Stability analysis of real time hybrid simulation under coupled actuator delay and nonlinear behavior

This paper deals with the global Mittag-Leffler stability (GMLS) of Caputo fractional-order fuzzy inertial neural networks with time delay (CFOFINND). Based on Lyapunov stability theory and global fractional Halanay inequalities, the existence of unique equilibrium point and GMLS of CFOFINND have been established. A numerical example is given to illustrate the effectiveness of our results.

Global Mittag-Leffler stability of Caputo fractional-order fuzzy inertial neural networks with delay

The dual consistency, which is an important issue in developing dual-weighted residual error estimation towards the goal-oriented mesh adaptivity, is studied in this paper both theoretically and numerically. Based on the Newton-GMG solver, dual consistency had been discussed in detail to solve the steady Euler equations. Theoretically, based on the Petrov-Galerkin method, the primal and dual problems, as well as the dual consistency, are deeply studied. It is found that dual consistency is important both for error estimation and stable convergence rate for the quantity of interest. Numerically, through the boundary modification technique, dual consistency can be guaranteed for the problem with general configuration. The advantage of taking care of dual consistency on the Newton-GMG framework can be observed clearly from numerical experiments, in which an order of magnitude savings of mesh grids can be expected for calculating the quantity of interest, compared with the dual-inconsistent implementation. Besides, the convergence behavior from the dual-consistent algorithm is stable, which guarantees the precisions would be better with the refinement in this framework.

Towards dual consistency of the dual weighted residual method based on a Newton-GMG framework for steady Euler equations

In this paper, we study the averaging principle for ψ-Capuo fractional stochastic delay differential equations (FSDDEs) with Poisson jumps. Based on fractional calculus, Burkholder-Davis-Gundy’s inequality, Doob’s martingale inequality, and the Ho¨lder inequality, we prove that the solution of the averaged FSDDEs converges to that of the standard FSDDEs in the sense of Lp. Our result extends some known results in the literature. Finally, an example and simulation is performed to show the effectiveness of our result.

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Jingfeng Wang

Papers

Global Lagrange stability for inertial neural networks with mixed time-varying delays

Stability analysis of real time hybrid simulation under coupled actuator delay and nonlinear behavior

Global Mittag-Leffler stability of Caputo fractional-order fuzzy inertial neural networks with delay

Towards dual consistency of the dual weighted residual method based on a Newton-GMG framework for steady Euler equations

Averaging Principle for ψ-Capuo Fractional Stochastic Delay Differential Equations with Poisson Jumps