Stability analysis of neural networks with time-varying delay using a new augmented Lyapunov–Krasovskii functional

Finite-time passivity of neutral-type complex-valued neural networks with time-varying delays

In this work, we investigated the finite-time passivity problem of neutral-type complex-valued neural networks with time-varying delays. On the basis of the Lyapunov functional, Wirtinger-type inequality technique, and linear matrix inequalities (LMIs) approach, new sufficient conditions were derived to ensure the finite-time boundedness (FTB) and finite-time passivity (FTP) of the concerned network model. At last, two numerical examples with simulations were presented to demonstrate the validity of our criteria.

Submission to Special Issue to Explainable Representation Learning-Based Intelligent Inspection and Maintenance of Complex Systems: Synchronization of Inertial Neural Networks With Unbounded Delays via Sampled-Data Control

This article addresses the synchronization issue for inertial neural networks (INNs) with heterogeneous time-varying delays and unbounded distributed delays, in which the state quantization is considered. First, by fully considering the delay and sampling time point information, a modified looped-functional is proposed for the synchronization error system. Compared with the existing Lyapunov-Krasovskii functional (LKF), the proposed functional contains the sawtooth structure term V8(t) and the time-varying terms ex(t-βħ (t)) and ey(t-βħ (t)) . Then, the obtained constraints may be further relaxed. Based on the functional and integral inequality, less conservative synchronization criteria are derived as the basis of controller design. In addition, the required quantized sampled-data controller is proposed by solving a set of linear matrix inequalities. Finally, two numerical examples are given to show the effectiveness and superiority of the proposed scheme in this article.

Synchronization of Stochastic Neural Networks Using Looped-Lyapunov Functional and Its Application to Secure Communication

This study aims to investigate the synchronization of user-controlled and uncontrolled neural networks (NNs) that exhibit chaotic solutions. The idea behind focusing on synchronization problems is to design the user-desired NNs by emulating the dynamical properties of traditional NNs rather than redefining them. Besides, instead of conventional NNs, this study considers NNs with significant factors such as time-dependent delays and uncertainties in the neural coefficients. In addition, information transmission over transmission may experience stochastic disturbances and network transmission. These factors will result in a stochastic differential NN model. Analyzing the NNs without these factors may be incompatible during the implementation. Theoretically, the model with stochastic disturbances can be considered a stochastic differential model, and the stability conditions are derived by employing Itô's formula and appropriate integral inequalities. To achieve synchronization, the sampled-data-based control scheme is proposed because it is more effective while information is being transmitted over networks. In contrast to the existing studies, this study contributes in terms of handling stochastic disturbances, effects of time-varying delays, and uncertainties in the system parameters via looped-type Lyapunov functional. Besides this, in the application view, delayed NNs are employed as a cryptosystem that helps to secure the transmission between the sender and the receiver, which is explored by illustrating the statistical measures evaluated for the standard images. From the simulation results, the proposed control and derived sufficient conditions can provide better synchronization and the proposed delayed NNs give a better cryptosystem.

A novel criteria on exponentially passive analysis for Takagi-Sugeno fuzzy of neutral dynamic system with various time-varying delays

This paper is the first studying on designing exponentially passive analysis for T-S fuzzy of dynamic systems with various time-varying delays such as neutral, discrete, and distributed time-varying delays. Constructing the new Lyapunov-Krasovskii function and the Newton-Leibniz theory, the zero equations, and the matrix inequality techniques, the multiple delay-dependent criteria, with assuring exponentially passive on the discussed T-S fuzzy system, are defined in respect of linear matrix inequalities (LMIs) that can be checked easily using the LMI toolbox of MATLAB. Those approaches give less conservative, exponentially passive criteria for special cases of general stability of a neutral differential system. Furthermore, the results of this study are delay-dependent, which depend on the lower and upper bound with the time-varying delay. Lastly, some numerical examples illustrate the performance of our criteria based on the results obtained and summarize some of the previous achievements.

Delay-Dependent Stability for Load Frequency Control System via Linear Operator Inequality

The stability analysis problem is considered for multiarea load frequency control (LFC) systems with electric vehicles (EVs) and time delays. The novel linear operator inequality approach is proposed and a less conservative delay-dependent stability condition is achieved. First, the model of the multiarea LFC system with EVs and delays is expressed by the partial integral equation (PIE) at the first time. Then, a complete quadratic Lyapunov-Krasovskii functional is built in the form of an inner product of the linear partial integral (PI) operator. The novel stability criteria with less conservatism are proposed in the form of linear operator inequality. Moreover, the relationships between the delay margins and the controller parameters are shown. Finally, the simulations are conducted on both one-area and two-area LFC systems to show the effectiveness of the proposed approach.

Some Novel Results on Stability Analysis of Generalized Neural Networks With Time-Varying Delays via Augmented Approach

This article proposes three new methods to enlarge the feasible region for guaranteeing stability for generalized neural networks having time-varying delays based on the Lyapunov method. First, two new zero equalities in which three states are augmented are proposed and inserted into the results of the time derivative of the constructed Lyapunov-Krasovskii functionals for the first time. Second, inspired by the Wirtinger-based integral inequality, new Lyapunov-Krasovskii functionals are introduced. Finally, by utilizing the relationship among the augmented vectors and from the original equation, newly augmented zero equalities are established and Finsler's lemma are applied. Through three numerical examples, it is verified that the proposed methods can contribute to enhance the allowable region of maximum delay bounds.

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.

Stability and dissipativity criteria for neural networks with time-varying delays via an augmented zero equality approach

This work investigates the stability and dissipativity problems for neural networks with time-varying delay. By the construction of new augmented Lyapunov-Krasovskii functionals based on integral inequality and the use of zero equality approach, three improved results are proposed in the forms of linear matrix inequalities. And, based on the stability results, the dissipativity analysis for NNs with time-varying delays was investigated. Through some numerical examples, the superiority and effectiveness of the proposed results are shown by comparing the existing works.

Finite-time non-fragile extended dissipative control for T-S fuzzy system via augmented Lyapunov-Krasovskii functional

The problem of non-fragile control for T-S fuzzy systems with parameter uncertainties is investigated in this paper. The focus is to construct an augmented Lyapunov-Krasovskii functional(LKF), single integral terms are processed by the method of an improved reciprocally convex inequality and integration by parts, which is derived to a new ht-depended stability criteria that finite-time bounded with extended dissipative for the closed-loop system. Furthermore, by using the linear matrix inequalities(LMIs), we can get the desired gain matrices of T-S fuzzy system. It is worth noting that these condition can derive to less conservative results than those existing approaches. And numerical examples are used to demonstrate the feasibility and superiority of the results.