Dissipativity Criteria Research Articles

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.

Dissipativity analysis for generalized neural networks with Markovian jump parameters and time-varying delay

This paper investigates the problem of delay-dependent dissipativity for a class of Markovian jump neural networks with a time-varying delay. A generalized integral inequality including some existing integral inequalities as special cases is established. An improved mode-dependent Lyapunov–Krasovskii functional (LKF) is constructed. Then, the new integral inequality is used to estimate the derivative of the LKF and a less conservative dissipativity criterion is derived. Based on the dissipativity criterion, a novel passivity condition for delayed neural networks is obtained. Furthermore, a new stability criterion for linear delayed systems without Markovian jump parameters is also developed. Finally, four numerical examples are presented to verify the effectiveness and superiority of the proposed method.

Delay-dependent dissipativity of neural networks with mixed non-differentiable interval delays

This paper investigates the global dissipativity and globally exponential dissipativity for neural networks with both interval time-varying delays and interval distributed time-varying delays. By constructing a set of appropriated Lyapunov–Krasovskii functionals and employing Newton–Leibniz formulation and free weighting matrix method, some dissipativity criteria that are dependent on the upper and lower bounds of the time-varying delays are derived in terms of linear matrix inequalities (LMIs), which can be easily verified via the LMI toolbox. Moreover, a positive invariant and globally attractive set is derived via the established LMIs. Finally, two numerical examples and their simulations are provided to demonstrate the effectiveness of the proposed criteria.

A potential-of-mean-force approach for fracture mechanics of heterogeneous materials using the lattice element method

Fracture of heterogeneous materials has emerged as a critical issue in many engineering applications, ranging from subsurface energy to biomedical applications, and requires a rational framework that allows linking local fracture processes with global fracture descriptors such as the energy release rate, fracture energy and fracture toughness. This is achieved here by means of a local and a global potential-of-mean-force (PMF) inspired Lattice Element Method (LEM) approach. In the local approach, fracture-strength criteria derived from the effective interaction potentials between mass points are shown to exhibit a scaling commensurable with the energy dissipation of fracture processes. In the global PMF-approach, fracture is considered as a sequence of equilibrium states associated with minimum potential energy states analogous to Griffith’s approach. It is found that this global approach has much in common with a Grand Canonical Monte Carlo (GCMC) approach, in which mass points are randomly removed following a maximum dissipation criterion until the energy release rate reaches the fracture energy. The duality of the two approaches is illustrated through the application of the PMF-inspired LEM for fracture propagation in a homogeneous linear elastic solid using different means of evaluating the energy release rate. Finally, by application of the method to a textbook example of fracture propagation in a heterogeneous material, it is shown that the proposed PMF-inspired LEM approach captures some well-known toughening mechanisms related to fracture energy contrast, elasticity contrast and crack deflection in the considered two-phase layered composite material.

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.

Effects of leakage delays and impulsive control in dissipativity analysis of Takagi–Sugeno fuzzy neural networks with randomly occurring uncertainties

In this paper, dissipativity analysis problem is investigated for T-S fuzzy neural networks with leakage delays and impulsive effects. Sufficient conditions for the dissipativity criteria are derived by using Lyapunov–Krasovskii functional having triple and four integral terms with free weighting matrix method. The obtained results are dependent on the the leakage delay and upper bound of time-varying delay. Moreover, some comparisons are made to contrast to some of existing results about strictly (Q,S,R)−ϑ-dissipativity for the concerned neural networks. Finally, some numerical examples and their computer simulations are given to show the effectiveness of the proposed criteria.

Synergistic interactions between silver decorated graphene and carbon nanotubes yield flexible composites to attenuate electromagnetic radiation

The need of today’s highly integrated electronic devices, especially working in the GHz frequencies, is to protect them from unwanted interference from neighbouring devices. Hence, lightweight, flexible, easy to process microwave absorbers were designed here by dispersing conductive multiwall carbon nanotubes (MWNTs) and silver nanoparticles decorated onto two-dimensional graphene sheets (rGO@Ag) in poly(ε-caprolactone) (PCL). In this study, we have shown how dielectric losses can be tuned in the nanocomposites by rGO@Ag nano-hybrid; an essential criterion for energy dissipation within a material resulting in effective shielding of the incoming electromagnetic (EM) radiation. Herein, the conducting pathway for nomadic charge transfer in the PCL matrix was established by MWNTs and the attenuation was tuned by multiple scattering due to the large specific surface area of rGO@Ag. The latter was possible because of the fine dispersion state of the Ag nanoparticles which otherwise often agglomerate if mixed separately. The effect of individual nanoparticles on microwave attenuation was systematically assessed here. It was observed that this strategy resulted in strikingly enhanced microwave attenuation in PCL nanocomposites in contrast to addition of individual particles. For instance, PCL nanocomposites containing both MWNTs and rGO@Ag manifested in a SET of −37 dB and, interestingly, at arelatively smaller fraction. The SE shown by this particular composite makes it a potential candidate for many commercial applications as reflected by its exceptional absorption capability (91.3%).

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.

Seismic response of precast structures with vertical cladding panels: The SAFECLADDING experimental campaign

The SAFECLADDING Project was aimed at improving the connection systems between cladding panels and precast RC buildings in seismic-prone areas. Three design criteria have been assessed: isostatic, dissipative and integrated. They can be realised using different strategies, which are represented by several test setups within the experimental campaign.The paper describes the results obtained with vertical panels arrangement and the comparison with the bare frame, which is the reference for the current design practice that considers panels like non-structural elements. The mock-up and the test sequence were designed to assess all setups with a single frame structure. The mock-up was a one-storey building, made by two parallel frames with two bays and square columns, inserted into pocket plinths. The building was designed for earthquake actions according to the Eurocode 8. Each setup was assessed using increasing levels of action, either with cyclic or pseudo-dynamic tests. The latter were performed both for serviceability and ultimate limit states. The experimental programme for vertical-panels and the bare-frame arrangement involved ten different setups, resulting in a total of twenty-eight tests.As for the isostatic criterion, the results confirm that considering panels as simple masses without stiffness is far from the real system behaviour, even using apposite devices to uncouple panels and frame displacements. In fact, despite a previous and positive experimental qualification, several devices failed in operative conditions tests.Conversely, the integrated criterion requires to bear high loads, transferred by the frame through connections, which becomes the weak point for this configuration, as demonstrated by different failures of bolts and connections.The reliability of the dissipative criterion has been confirmed by twelve tests completed without any damage. This solution in fact combines lower relative displacements with limited loads within connections, avoiding both the compatibility problems and excessive forces.

Reprint of: Dynamics of discrete screw dislocations on glide directions

We consider a simple discrete model for screw dislocations in crystals. Using a variational discrete scheme we study the motion of a configuration of dislocations toward low energy configurations. We deduce an effective fully overdamped dynamics that follows the maximal dissipation criterion introduced in Cermelli and Gurtin (1999) and predicts motion along the glide directions of the crystal.

Dynamics of screw dislocations: A generalised minimising-movements scheme approach

The gradient flow structure of the model introduced in Cermelli & Gurtin (1999, The motion of screw dislocations in crystalline materials undergoing antiplane shear: glide, cross-slip, fine cross-slip. Arch. Rational Mech. Anal.148(1), 3–52) for the dynamics of screw dislocations is investigated by means of a generalised minimising-movements scheme approach. The assumption of a finite number of available glide directions, together with the “maximal dissipation criterion” that governs the equations of motion, results into solving a differential inclusion rather than an ODE. This paper addresses how the model in Cermelli & Gurtin is connected to a time-discrete evolution scheme which explicitly confines dislocations to move at each time step along a single glide direction. It is proved that the time-continuous model in Cermelli & Gurtin is the limit of these time-discrete minimising-movement schemes when the time step converges to 0. The study presented here is a first step towards a generalisation of standard gradient flow theory that allows for dissipations which cannot be described by a metric.

An Improved Result on Dissipativity and Passivity Analysis of Markovian Jump Stochastic Neural Networks With Two Delay Components.

In this paper, we investigate the dissipativity and passivity of Markovian jump stochastic neural networks involving two additive time-varying delays. Using a Lyapunov-Krasovskii functional with triple and quadruple integral terms, we obtain delay-dependent passivity and dissipativity criteria for the system. Using a generalized Finsler lemma (GFL), a set of slack variables with special structure are introduced to reduce design conservatism. The dissipativity and passivity criteria depend on the upper bounds of the discrete time-varying delay and its derivative are given in terms of linear matrix inequalities, which can be efficiently solved through the standard numerical software. Finally, our illustrative examples show that the proposed method performs well and is successful in problems where existing methods fail.

Further Results on Dissipativity Criterion for Markovian Jump Discrete-Time Neural Networks with Two Delay Components Via Discrete Wirtinger Inequality Approach

This paper is concerned with strict $$(\mathcal {Q}, \mathcal {S}, \mathcal {R})-\gamma $$(Q,S,R)-? - dissipativity and passivity analysis for discrete-time Markovian jump neural networks involving both leakage and discrete delays expressed in terms of two additive time-varying delay components. The discretized Wirtinger inequality is utilized to bound the forward difference of finite-sum term in the Lyapunov functional. By constructing a suitable Lyapunov---Krasovskii functional, sufficient conditions are derived to guarantee the dissipativity and passivity criteria of the proposed neural networks. These conditions are presented in terms of linear matrix inequalities (LMIs), which can be efficiently solved via LMI MATLAB Toolbox. Finally, numerical examples are given to illustrate the effectiveness of the proposed results.

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.

Dissipativity analysis of stochastic memristor-based recurrent neural networks with discrete and distributed time-varying delays

ABSTRACTIn this paper, based on the knowledge of memristor-based recurrent neural networks (MRNNs), the model of the stochastic MRNNs with discrete and distributed delays is established. In real nervous systems and in the implementation of very large-scale integration (VLSI) circuits, noise is unavoidable, which leads to the stochastic model of the MRNNs. In this model, the delay interval is decomposed into two subintervals by using the tuning parameter α such that 0 < α < 1. By constructing proper Lyapunov–Krasovskii functional and employing direct delay decomposition technique, several sufficient conditions are given to guarantee the dissipativity and passivity of the stochastic MRNNs with discrete and distributed delays in the sense of Filippov solutions. Using the stochastic analysis theory and Itô’s formula for stochastic differential equations, we establish sufficient conditions for dissipativity criterion. The dissipativity and passivity conditions are presented in terms of linear matrix inequalities, which can be easily solved by using Matlab Tools. Finally, three numerical examples with simulations are presented to demonstrate the effectiveness of the theoretical results.

Dynamics of discrete screw dislocations on glide directions

We consider a simple discrete model for screw dislocations in crystals. Using a variational discrete scheme we study the motion of a configuration of dislocations toward low energy configurations. We deduce an effective fully overdamped dynamics that follows the maximal dissipation criterion introduced in Cermelli and Gurtin (1999) and predicts motion along the glide directions of the crystal.

Delay-dependent stability and dissipativity analysis of generalized neural networks with Markovian jump parameters and two delay components

This paper focuses on the problem of delay-dependent stability and dissipativity analysis of generalized neural networks (GNNs) with Markovian jump parameters and two delay components. By constructing novel augmented Lyapunov–Krasovskii functional (LKF), using free-matrix-based inequality to estimate the derivative of Lyapunov function and employing the reciprocally convex approach to consider the relationship between the time-varying delay and its interval, some improved delay-dependent stability criteria and dissipativity criteria are established in terms of linear matrix inequalities. Moreover, the obtained criteria is extended to analyze the stability analysis of GNNs with two delay components and the passivity analysis of GNNs with one delay. Numerical examples are given to show the effectiveness and the significant improvement of the proposed methods.

An overview of some recent results on the Euler system of isentropic gas dynamics

This overview is concerned with the well-posedness problem for the isentropic compressible Euler equations of gas dynamics. The results we present are in line with the programof investigatingthe efficiency of different selection criteria proposed in the literature in order to weed out non-physical solutions to more-dimensional systems of conservation laws and they build upon the method of convex integration developed by De Lellis and Szekelyhidi for the incompressible Euler equations. Mainly following [5], we investigate the role of the maximal dissipation criterion proposed by Dafermos in [6]: we prove how, for specific pressure laws, some non-standard (i.e. constructed via convex integration methods) solutions to the Riemann problem for the isentropic Euler system in two space dimensions have greater energy dissipation rate than the classical self-similar solution emanating from the same Riemann data. We therefore show that the maximal dissipation criterion proposed by Dafermos does not favour in general the self-similar solutions.

Кривые длительной прочности нелинейной модели вязкоупругопластичности типа Максвелла и правило суммирования поврежденности при ступенчатых нагружениях

Исследуется нелинейное определяющее соотношение типа Максвелла для вязкоупругопластичных материалов с двумя произвольными материальными функциями одного аргумента с целью выявления арсенала его возможностей и области применимости, в частности, возможности подключения к нему критериев для описания разрушения при ползучести с постоянным или кусочно-постоянным напряжением. При минимальных первичных ограничениях на материальные функции выведены уравнения теоретических кривых длительной прочности, порожденных соотношением типа Максвелла в сочетании с деформационными и энергетическим (диссипативным) критериями разрушения, а также с интегральными критериями, учитывающими историю деформирования. Аналитически изучены и сопоставлены общие свойства этих кривых. Показано, что они адекватно описывают типичные свойства экспериментальных кривых длительной прочности вязкоупругопластических материалов. Для найденных зависимостей времен разрушения от напряжения проверено выполнение правила линейного накопления поврежденности при ступенчатом нагружении и выведены формулы для величины (и знака) отклонений от него. В частности доказано, что для нелинейного соотношения типа Максвелла в сочетании с диссипативным критерием разрушения всегда в точности выполняется правило линейного накопления поврежденности при любом ступенчатом нагружении, а для деформационного критерия оно, наоборот, никогда не выполняется, но дает оценку сверху или снизу для времени разрушения в зависимости от знака скачка напряжения.