A delay partitioning approach to delay-dependent stability analysis for neutral type neural networks with discrete and distributed delays

The combined Lyapunov functionals method for stability analysis of neutral Cohen-Grossberg neural networks with multiple delays

This research article will employ the combined Lyapunov functionals method to deal with stability analysis of a more general type of Cohen-Grossberg neural networks which simultaneously involve constant time and neutral delay parameters. By utilizing some combinations of various Lyapunov functionals, we determine novel criteria ensuring global stability of such a model of neural systems that employ Lipschitz continuous activation functions. These proposed results are totally stated independently of delay terms and they can be completely characterized by the constants parameters involved in the neural system. By making some detailed analytical comparisons between the stability results derived in this research article and the existing corresponding stability criteria obtained in the past literature, we prove that our proposed stability results lead to establishing some sets of stability conditions and these conditions may be evaluated as different alternative results to the previously reported corresponding stability criteria. A numerical example is also presented to show the applicability of the proposed stability results.

Finite-Time Passivity Analysis of Neutral-Type Neural Networks with Mixed Time-Varying Delays

This research study investigates the issue of finite-time passivity analysis of neutral-type neural networks with mixed time-varying delays. The time-varying delays are distributed, discrete and neutral in that the upper bounds for the delays are available. We are investigating the creation of sufficient conditions for finite boundness, finite-time stability and finite-time passivity, which has never been performed before. First, we create a new Lyapunov–Krasovskii functional, Peng–Park’s integral inequality, descriptor model transformation and zero equation use, and then we use Wirtinger’s integral inequality technique. New finite-time stability necessary conditions are constructed in terms of linear matrix inequalities in order to guarantee finite-time stability for the system. Finally, numerical examples are presented to demonstrate the result’s effectiveness. Moreover, our proposed criteria are less conservative than prior studies in terms of larger time-delay bounds.

New criteria for global stability of neutral-type Cohen-Grossberg neural networks with multiple delays

The significant contribution of this paper is the addressing the stability issue of neutral-type Cohen-Grossberg neural networks possessing multiple time delays in the states of the neurons and multiple neutral delays in time derivative of states of the neurons. By making the use of a novel and enhanced Lyapunov functional, some new sufficient stability criteria are presented for this model of neutral-type neural systems. The obtained stability conditions are completely dependent of the parameters of the neural system and independent of time delays and neutral delays. A constructive numerical example is presented for the sake of proving the key advantages of the proposed stability results over the previously reported corresponding stability criteria for Cohen-Grossberg neural networks of neutral type. Since, stability analysis of Cohen-Grossberg neural networks involving multiple time delays and multiple neutral delays is a difficult problem to overcome, the investigations of the stability conditions of the neutral-type the stability analysis of this class of neural network models have not been given much attention. Therefore, the stability criteria derived in this work can be evaluated as a valuable contribution to the stability analysis of neutral-type Cohen-Grossberg neural systems involving multiple delays.

Stability Analysis for Delayed Neural Networks With an Improved General Free-Matrix-Based Integral Inequality

This paper revisits the problem of stability analysis for neural networks with a time-varying delay. An improved general free-matrix-based (FMB) integral inequality is proposed with an undetermined number m . Compared with the conventional FMB ones, the improved inequality involves a much smaller number of free matrix variables. In particular, the improved FMB integral inequality is expressed in a concrete form for any value of m . By employing the new inequality with a properly constructed Lyapunov-Krasovskii functional, a new stability condition is derived for neural networks with a time-varying delay. Two commonly used numerical examples are given to show strong competitiveness of the proposed approach in both the conservatism and computation burdens.

Some generalized global stability criteria for delayed Cohen-Grossberg neural networks of neutral-type

This paper carries out a theoretical investigation into the stability problem for the class of neutral-type Cohen-Grossberg neural networks with discrete time delays in states and discrete neutral delays in time derivative of states. By employing a more general type of suitable Lyapunov functional, a set of new generalized sufficient criteria are derived for the global asymptotic stability of delayed neural networks of neutral-type. The proposed stability criteria are independently of the values of the time delays and neutral delays, and they completely rely on some algebraic mathematical relationships involving the values of the elements of the interconnection matrices and the other network parameters. Therefore, it is easy to verify the validity of the obtained results by simply using some algebraic equations representing the stability conditions. A detailed comparison between our proposed results and recently reported corresponding stability results is made, proving that the results given in this paper generalize previously published stability results. A constructive numerical example is also given to demonstrate the applicability of the results of the paper.

Hierarchical Stability Conditions for a Class of Generalized Neural Networks With Multiple Discrete and Distributed Delays

This brief investigates the analysis issue for global asymptotic stability of a class of generalized neural networks with multiple discrete and distributed delays. To tackle delays arising in different neuron activation functions, we employ a generalized model with multiple discrete and distributed delays which covers various existing neural networks. We then generalize the Bessel-Legendre inequalities to deal with integral terms with any linearly independent functions and nonlinear function of states. Based on these inequalities, we design the Lyapunov-Krasovskii functional and derive hierarchical linear matrix inequality stability conditions. Finally, three numerical examples are provided to demonstrate that the proposed method is less conservative with a reasonable numerical burden than the existing results.

Robust H∞ state-feedback control for linear systems

This paper investigates the problem of robust H∞ control for linear systems. First, the state-feedback closed-loop control algorithm is designed. Second, by employing the geometric progression theory, a modified augmented Lyapunov-Krasovskii functional (LKF) with the geometric integral interval is established. Then, parameter uncertainties and the derivative of the delay are flexibly described by introducing the convex combination skill. This technique can eliminate the unnecessary enlargement of the LKF derivative estimation, which gives less conservatism. In addition, the designed controller can ensure that the linear systems are globally asymptotically stable with a guaranteed H∞ performance in the presence of a disturbance input and parameter uncertainties. A liquid monopropellant rocket motor with a pressure feeding system is evaluated in a simulation example. It shows that this proposed state-feedback control approach achieves the expected results for linear systems in the sense of the prescribed H∞ performance.

Synchronization of Neural Networks With Control Packet Loss and Time-Varying Delay via Stochastic Sampled-Data Controller

This paper addresses the problem of exponential synchronization of neural networks with time-varying delays. A sampled-data controller with stochastically varying sampling intervals is considered. The novelty of this paper lies in the fact that the control packet loss from the controller to the actuator is considered, which may occur in many real-world situations. Sufficient conditions for the exponential synchronization in the mean square sense are derived in terms of linear matrix inequalities (LMIs) by constructing a proper Lyapunov-Krasovskii functional that involves more information about the delay bounds and by employing some inequality techniques. Moreover, the obtained LMIs can be easily checked for their feasibility through any of the available MATLAB tool boxes. Numerical examples are provided to validate the theoretical results.

Stability criteria for recurrent neural networks with time-varying delay based on secondary delay partitioning method

A secondary delay partitioning method is proposed to study the stability problem for a class of recurrent neural networks (RNNs) with time-varying delay. The total interval of the time-varying delay is first divided into two parts, and then each part is further divided into several subintervals. To deal with the state variables associated with these subintervals, an extended reciprocal convex combination approach and a double integral term with variable upper and lower limits of integral as a Lyapunov functional are proposed, which help to obtain the stability criterion. The main feature of the proposed result is more effective for the RNNs with fast time-varying delay. A numerical example is used to show the effectiveness of the proposed stability result.

Stability analysis of neutral type neural networks with mixed time-varying delays using triple-integral and delay-partitioning methods

This paper investigates the asymptotical stability problem for a class of neutral type neural networks with mixed time-varying delays. The system not only has time-varying discrete delay, but also distributed delay, which has never been discussed in the previous literature. Firstly, improved stability criteria are derived by employing the more general delay partitioning approach and generalizing the famous Jensen inequality. Secondly, by constructing a newly augmented Lyapunov-Krasovskii functionals, some less conservative stability criteria are established in terms of linear matrix inequalities (LMIs). Finally, four numerical examples are given to illustrate the effectiveness and the advantage of the proposed main results.

Stability Analysis of Distributed Delay Neural Networks Based on Relaxed Lyapunov-Krasovskii Functionals

This paper revisits the problem of asymptotic stability analysis for neural networks with distributed delays. The distributed delays are assumed to be constant and prescribed. Since a positive-definite quadratic functional does not necessarily require all the involved symmetric matrices to be positive definite, it is important for constructing relaxed Lyapunov-Krasovskii functionals, which generally lead to less conservative stability criteria. Based on this fact and using two kinds of integral inequalities, a new delay-dependent condition is obtained, which ensures that the distributed delay neural network under consideration is globally asymptotically stable. This stability criterion is then improved by applying the delay partitioning technique. Two numerical examples are provided to demonstrate the advantage of the presented stability criteria.