Extended Dissipativity Criterion Research Articles

Extended dissipative analysis for memristive neural networks with two-delay components via a generalized delay-product-type Lyapunov-Krasovskii functional

<abstract><p>In this study, we deal with the problem of extended dissipativity analysis for memristive neural networks (MNNs) with two-delay components. The goal is to get less conservative extended dissipativity criteria for delayed MNNs. An improved Lyapunov-Krasovskii functional (LKF) with some generalized delay-product-type terms is constructed based on the dynamic delay interval (DDI) method. Moreover, the derivative of the created LKF is estimated using the integral inequality technique, which includes the information of higher-order time-varying delay. Then, sufficient conditions are attained in terms of linear matrix inequalities (LMIs) to pledge the extended dissipative of MNNs via the new negative definite conditions of matrix-valued cubic polynomials. Finally, a numerical example is shown to prove the value and advantage of the presented approach.</p></abstract>

Non-fragile extended dissipative state estimation for delayed discrete-time neural networks: application to quadruple tank process model

This paper deals with the non-fragile state estimator design to study the robust extended dissipativity criterion for a class of discrete-time neural networks (DNNs) involving uncertainties as well as time-varying delay components. The requisite of the proposed problem is to design a proper state estimator such that the dynamics of the corresponding estimation error is extended dissipative having external disturbance and unpredictable fragility performance. By constructing an appropriate Lyapunov–Krasovskii functional (LKF), the sufficient conditions for the extended dissipativity performance of the error system obtained by means of the proposed DNNs and its estimator which includes the $$H_{\infty }$$ performance, $$L_{2}-L_{\infty }$$ performance, passivity and dissipativity performance in a unified framework. The established theoretical results are expressed in terms of linear matrix inequalities (LMIs) that can be easily checked by using the standard numerical softwares. In order to analyze the applicability and effectiveness of the proposed theoretical results, numerical examples including a quadruple tank process (QTP) system model have been illustrated with simulation results.

Novel extended dissipativity criteria for generalized neural networks with interval discrete and distributed time-varying delays

The problem of asymptotic stability and extended dissipativity analysis for the generalized neural networks with interval discrete and distributed time-varying delays is investigated. Based on a suitable Lyapunov–Krasovskii functional (LKF), an improved Wirtinger single integral inequality, a novel triple integral inequality, and convex combination technique, the new asymptotic stability and extended dissipativity criteria are achieved for the generalized neural networks with interval discrete and distributed time-varying delays. By the above methods, the less conservative asymptotic stability criteria are obtained for a special case of the generalized neural networks. By using the Matlab LMI toolbox, the derived new asymptotic stability and extended dissipativity criteria are expressed in terms of linear matrix inequalities (LMIs) that cover H_{infty }, L_{2}–L_{infty }, passivity, and dissipativity performance by setting parameters in the general performance index. Finally, we show numerical examples which are less conservative than other examples in the literature. Moreover, we present numerical examples for asymptotic stability and extended dissipativity performance of the generalized neural networks, including a special case of the generalized neural networks.

A linear matrix inequality-based extended dissipativity criteria for linear systems with additive time-varying delays

In this paper, the problem of extended dissipativity performance has been investigated for a class of linear systems with additive time-varying delays. By constructing an appropriate Lyapunov Krasovskii functional (LKF) with triple and quadruple integral terms, a delay dependent extended dissipativity criterion which specifies H∞, dissipativity, passivity and l2−l∞ performance has been established. The obtained delay derivative dependent extended dissipativity results have been presented in terms of linear matrix inequalities (LMIs) which can be efficiently solved via some standard numerical softwares. Finally, some numerical examples are provided to verify the effectiveness of the presented results.

Finite-time extended dissipativity of delayed Takagi–Sugeno fuzzy neural networks using a free-matrix-based double integral inequality

This study focuses on the finite-time extended dissipativity of delayed Takagi–Sugeno (T–S) fuzzy neural networks (NNs). Based on the concept of extended dissipativity, this paper solves the $$H_\infty$$ , $$L_2-L_\infty$$ , passive, and $$({{\mathcal {Q}}}, {{\mathcal {S}}}, {\mathcal {R}})$$ -dissipativity performance in a unified framework. Using the free-matrix-based double integral inequality and an extended Wirtinger inequality in the Lyapunov–Krasovskii functional, sufficient conditions are derived to guarantee that the considered NNs are finite-time bounded, whereupon the finite-time extended dissipativity criteria for delayed T–S fuzzy NNs are constructed. The derived conditions guarantee the extended dissipativity and stability of the NNs. Three numerical examples are given to demonstrate the reduced conservatism and the effectiveness of the obtained results.

Extended Dissipativity Analysis for Markovian Jump Neural Networks With Time-Varying Delay via Delay-Product-Type Functionals.

This paper investigates the problem of extended dissipativity for Markovian jump neural networks (MJNNs) with a time-varying delay. The objective is to derive less conservative extended dissipativity criteria for delayed MJNNs. Toward this aim, an appropriate Lyapunov-Krasovskii functional (LKF) with some improved delay-product-type terms is first constructed. Then, by employing the extended reciprocally convex matrix inequality (ERCMI) and the Wirtinger-based integral inequality to estimate the derivative of the constructed LKF, a delay-dependent extended dissipativity condition is derived for the delayed MJNNs. An improved extended dissipativity criterion is also given via the allowable delay sets method. Based on the above-mentioned results, the extended dissipativity condition of delayed NNs without Markovian jump parameters is directly derived. Finally, three numerical examples are employed to illustrate the advantages of the proposed method.

Extended dissipativity analysis for discrete-time delayed neural networks based on an extended reciprocally convex matrix inequality

In this paper, the extended dissipativity analysis for discrete-time neural networks with a time-varying delay is investigated. First, a novel Lyapunov–Krasovskii functional (LKF) is constructed with a delay-product-type term introduced. Then, in the forward difference of the LKF, the sum terms are bounded via an extended reciprocally convex matrix inequality. As a result, an extended dissipativity criterion is established in terms of linear matrix inequalities. Meanwhile, this criterion is extended to the stability analysis of the counterpart system without disturbance. Finally, two numerical examples are given to demonstrate the effectiveness and improvements of the presented criterion.

Exponential stability and extended dissipativity criteria for generalized discrete-time neural networks with additive time-varying delays

This paper is concerned with exponential stability and extended dissipativity criteria for generalized discrete-time neural networks (GDNNs) with additive time-varying delays. The generalized dissipativity analysis combines a few previous results into a framework, such as l2−l∞ performance, H∞ performance, passivity performance, strictly (Q,S,R)−γ−dissipative and strictly (Q,S,R)−dissipative. The definition of exponential stability for GDNNs is given with a new and more appropriate expression. A novel augmented Lyapunov-Krasovskii functional (LKF) which involves more information about the additive time-varying delays is constructed. By introducing more zero equalities and using a new double summation inequality together with Finsler’s lemma, an improved delay-dependent exponential stability and extended dissipativity criterion are derived in terms of convex combination technique (CCT). Finally, numerical examples are given to illustrate the usefulness and advantages of the proposed methods.

Exponential stabilization for fuzzy sampled-data system based on a unified framework and its application

This article deals with the exponential stabilization problems of Takagi–Sugeno (T–S) fuzzy system under aperiodic sampling. The objective is to solve the H∞, L2−L∞, passive and dissipative stability and stabilization problems based on a unified performance index-extended dissipativity. Some new stability conditions consisting of both exponential stability and extended dissipativity criterion are first established. A sampling period dependent Lyapunov–Krasovskii function together with a novel efficient integral inequality, which has the advantage of reducing conservativeness, is adopted. On the basis of the stability conditions, a sampled-data controller that can not only exponentially stabilize the system but also guarantee the prescribed extended-dissipativity performance is then designed. Moreover, an exponential decay rate can be set in advance to achieve better system performance. Finally, a quarter-vehicle active suspension system with considering payload uncertainties and aperiodic sampling is provided for evaluating the validity and superiority of the extended dissipative control approach proposed in this article.

Robust extended dissipativity criteria for discrete-time uncertain neural networks with time-varying delays

In this draft, we consider the problem of robust extended dissipativity for uncertain discrete-time neural networks (DNNs) with time-varying delays. By constructing appropriate Lyapunov–Krasovskii functional (LKF), sufficient conditions are established to ensure that the considered time-delayed uncertain DNN is extended dissipative. The derived conditions are presented in terms of linear matrix inequalities (LMIs). Numerical examples are provided to illustrate the superiority of this result.

Exponential stability and extended dissipativity criteria for generalized neural networks with interval time-varying delay signals

This paper discusses the problems of exponential stability and extended dissipativity analysis of generalized neural networks (GNNs) with time delays. A new criterion for the exponential stability and extended dissipativity of GNNs is established based on the suitable Lyapunov–Krasovskii functionals (LKFs) together with the Wirtinger single integral inequality (WSII) and Wirtinger double integral inequality (WDII) technique, and that is mixed with the reciprocally convex combination (RCC) technique. An improved exponential stability and extended dissipativity criterion for GNNs are expressed in terms of linear matrix inequalities (LMIs). The major contributions of this study are an exponential stability and extended dissipativity concept can be developed to analyze simultaneously the solutions of the exponential H∞, L2−L∞, passivity, and dissipativity performance for GNNs by selecting the weighting matrices. Finally, several interesting numerical examples are developed to verify the usefulness of the proposed results, among them one example was supported by real-life application of the benchmark problem that associates with reasonable issues under extended dissipativity performance.

Extended dissipative state estimation for uncertain discrete-time Markov jump neural networks with mixed time delays

This paper is concerned with the problem of extended dissipativity-based state estimation for uncertain discrete-time Markov jump neural networks with finite piecewise homogeneous Markov chain and mixed time delays. The aim of this paper is to present a Markov switching estimator design method, which ensures that the resulting error system is extended stochastically dissipative. A triple-summable term is introduced in the constructed Lyapunov function and the reciprocally convex approach is utilized to bound the forward difference of the triple-summable term. The extended dissipativity criterion is derived in form of linear matrix inequalities. Numerical simulations are conducted to demonstrate the effectiveness of the proposed method.

Extended dissipative analysis for memristive neural networks with two additive time-varying delay components

This paper concentrates on the extended dissipativity of memristive neural networks with two additive time-varying delays. After giving a foundation to the memristive model, the paper establishes some fundamental results on quadratically stability and extended dissipativity criteria by means of the Lyapunov functional, integral inequality, as well as the relationship between time-varying delays. The novel extended dissipative inequality contains several weighting matrices, by converting the weighting matrices in a new performance index, the extended dissipativity will be degraded to the H∞ performance, L2−L∞ performance, passivity and dissipativity, respectively. Finally, one example is given to substantiate the significant improvement of the theoretical approaches.

On Extended Dissipativity of Discrete-Time Neural Networks With Time Delay.

In this brief, the problem of extended dissipativity analysis for discrete-time neural networks with time-varying delay is investigated. The definition of extended dissipativity of discrete-time neural networks is proposed, which unifies several performance measures, such as the H∞ performance, passivity, l2 - l∞ performance, and dissipativity. By introducing a triple-summable term in Lyapunov function, the reciprocally convex approach is utilized to bound the forward difference of the triple-summable term and then the extended dissipativity criterion for discrete-time neural networks with time-varying delay is established. The derived condition guarantees not only the extended dissipativity but also the stability of the neural networks. Two numerical examples are given to demonstrate the reduced conservatism and effectiveness of the obtained results.