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

State Estimation for Complex-Valued Inertial Neural Networks with Multiple Time Delays

In this paper, the problem of state estimation for complex-valued inertial neural networks with leakage, additive and distributed delays is considered. By means of the Lyapunov–Krasovskii functional method, the Jensen inequality, and the reciprocally convex approach, a delay-dependent criterion based on linear matrix inequalities (LMIs) is derived. At the same time, the network state is estimated by observing the output measurements to ensure the global asymptotic stability of the error system. Finally, two examples are given to verify the effectiveness of the proposed method.

Anti-Synchronization of Delayed State-Based Switched Inertial Neural Networks

In this article, global anti-synchronization control for a class of state-based switched inertial neural networks (SBSINNs) with time-varying delays is considered. Based on the hybrid control strategies and Lyapunov stability theory, several criteria are obtained to ensure global anti-synchronization of the underlying SBSINNs. Furthermore, we consider the global asymptotic anti-synchronization directly from the SBSINNs themselves with a nonreduced-order method. Finally, a numerical simulation is given to illustrate the effectiveness of the results.

Novel results on finite-time stabilization of state-based switched chaotic inertial neural networks with distributed delays

The p-norm finite-time stabilization (FTS) issue of a class of state-based switched inertial chaotic neural networks (SBSCINNs) with distributed time-varying delays is investigated. By using a suitable variable transformation, such second-order SBSCINNs are turned into the first-order differential equations. Then some novel criteria are obtained to stabilize SBSCINNs in a finite time based on the theory of finite-time control and non-smooth analysis together with designing two proper delay-dependent feedback controllers. Besides, the settling time of FTS is also estimated and discussed. Finally, the validity and practicability of the deduced theoretical results are verified by examples and applications.

Stabilization of Second-Order Memristive Neural Networks With Mixed Time Delays via Nonreduced Order

In this brief, we investigate a class of second-order memristive neural networks (SMNNs) with mixed time-varying delays. Based on nonsmooth analysis, the Lyapunov stability theory, and adaptive control theory, several new results ensuring global stabilization of the SMNNs are obtained. In addition, compared with the reduced-order method used in the existing research studies, we consider the global stabilization directly from the SMNNs themselves without the reduced-order method. Finally, we give some numerical simulations to show the effectiveness of the results.

Periodicity of non-autonomous inertial neural networks involving proportional delays and non-reduced order method

This paper, mainly explores a class of non-autonomous inertial neural networks with proportional delays and time-varying coefficients. By combining Lyapunov function method with differential inequality approach, non-reduced order method is used to establish some novel assertions on the existence and generalized exponential stability of periodic solutions for the addressed model. In addition, an example and its numerical simulations are given to support the proposed approach.

Stability Analysis of Quaternion-Valued Neutral-Type Neural Networks with Time-Varying Delay

This paper addresses the problem of global μ -stability for quaternion-valued neutral-type neural networks (QVNTNNs) with time-varying delays. First, QVNTNNs are transformed into two complex-valued systems by using a transformation to reduce the complexity of the computation generated by the non-commutativity of quaternion multiplication. A new convex inequality in a complex field is introduced. In what follows, the condition for the existence and uniqueness of the equilibrium point is primarily obtained by the homeomorphism theory. Next, the global stability conditions of the complex-valued systems are provided by constructing a novel Lyapunov–Krasovskii functional, using an integral inequality technique, and reciprocal convex combination approach. The gained global μ -stability conditions can be divided into three different kinds of stability forms by varying the positive continuous function μ ( t ) . Finally, three reliable examples and a simulation are given to display the effectiveness of the proposed methods.

Quantized Sampled-Data Control for Synchronization of Inertial Neural Networks With Heterogeneous 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.

Passivity analysis of memristor-based impulsive inertial neural networks with time-varying delays

This paper focuses on delay-dependent passivity analysis for a class of memristive impulsive inertial neural networks with time-varying delays. By choosing proper variable transformation, the memristive inertial neural networks can be rewritten as first-order differential equations. The memristive model presented here is regarded as a switching system rather than employing the theory of differential inclusion and set-value map. Based on matrix inequality and Lyapunov-Krasovskii functional method, several delay-dependent passivity conditions are obtained to ascertain the passivity of the addressed networks. In addition, the results obtained here contain those on the passivity for the addressed networks without impulse effects as special cases and can also be generalized to other neural networks with more complex pulse interference. Finally, one numerical example is presented to show the validity of the obtained results.