Dissipativity Criteria Research Articles

A new convex integration approach for the compressible Euler equations and failure of the local maximal dissipation criterion

Abstract In this paper we establish a new convex integration approach for the barotropic compressible Euler equations in two space dimensions. In contrast to existing literature, our new method generates not only the momentum for given density, but also the energy and the energy flux. This allows for a simple way to construct admissible solutions, i.e. solutions which satisfy the energy inequality. Moreover using the convex integration method developed in this paper, we show that the local maximal dissipation criterion fails in the following sense: There exist wild solutions which beat the self-similar solution of the one-dimensional Riemann problem extended to two dimensions. Hence the local maximal dissipation criterion rules out the self-similar solution. The convex integration machinery itself is carried out in a very general way. Hence this paper provides a universal framework for convex integration which not even specifies the form of the partial differential equations under consideration. Therefore this general framework is applicable in many different situations.

A new inequality and its application in descriptor Markovian jump systems with time-varying delays

This paper is focused on the dissipativity analysis of descriptor Markovian jump systems with time-varying delays. For achieving this aim, an augmented mode-dependent Lyapunov-Krasovskii functional (LKF) is constructed on the basis of the state decomposition method. Next, a novel integral inequality is proposed through the generalized free-weighting-matrix (GFWM) method as well as zero-valued equalities to estimate single integral terms more precisely. Then, an ameliorative stochastic admissibility and dissipative criterion is derived by utilizing the proposed integral inequality, the augmented LKF and other bounding techniques. Finally, the effectiveness and superiority of the presented results are confirmed with some numerical examples.

Dissipative sliding mode tracking control for discrete-time singular T-S fuzzy systems via a preview target mechanism

This study focuses on the dissipative sliding mode preview tracking control (SMPTC) of discrete-time singular T-S fuzzy systems (STSFSs) via a preview target mechanism. Due to the presence of singular matrix and input matrices with fuzzy rules in the system, the existing preview control approaches cannot be directly adopted. As a result, a novel singular augmented error system (AES) is derived based on a general method. Furthermore, the tracking problem has been translated into the stabilisation of singular AES. A linear sliding mode surface (SMS) is proposed for singular AES, and a suitably SMPTC law is presented. Sufficiency conditions for relaxation are derived to guarantee that the sliding mode dynamics is admissible with the dissipative criterion, and the sliding mode region (SMR) can be reached. The difference singular matrix is fully considered in the whole design process such that the derived conditions can be checked easily. Finally, two examples have shown the effective tracking of the original output signal of system by utilising the proposed SMPTC law.

Extended dissipative criteria for delayed semi-discretized competitive neural networks

This brief investigates the extended dissipativity performance of semi-discretized competitive neural networks (CNNs) with time-varying delays. Inspired by the computational efficiency and feasibility of implementing the networks, we formulate a discrete counterpart to the continuous-time CNNs. By employing an appropriate Lyapunov–Krasovskii functional (LKF) and a relaxed summation inequality, sufficient conditions ensure the extended dissipative criteria of discretized CNNs are obtained in the linear matrix inequality framework. Finally, to refine our prediction, two numerical examples are provided to demonstrate the sustainability and merits of the theoretical results.

Novel passivity and dissipativity criteria for discrete-time fractional generalized delayed Cohen–Grossberg neural networks

This paper pays attention to the passivity and dissipativity for discrete-time fractional generalized delayed Cohen-Grossberg neural networks. A new fractional passive lemma is firstly proposed for discrete-time system by means of the Lyapunov functional. This facilitates the discussion of system stabilization in terms of input and output energy. Some passive and dissipative conditions are established under comparison principle, reduction to absurdity, inequality techniques and the proposed passive lemma. Finally, two examples are performed to demonstrate the validity of proposed methods.

The semi-implicit DLN algorithm for the Navier-Stokes equations

AbstractDahlquist, Liniger, and Nevanlinna design a family of one-leg, two-step methods (the DLN method) that is second order, $$\varvec{A}-$$ A - and $$\varvec{G}-$$ G - stable for arbitrary, non-uniform time steps. Recently, the implementation of the DLN method can be simplified by the refactorization process (adding time filters on the backward Euler scheme). Due to these fine properties, the DLN method has strong potential for the numerical simulation of time-dependent fluid models. In the report, we propose a semi-implicit DLN algorithm for the Navier-Stokes equations (avoiding non-linear solver at each time step) and prove the unconditional, long-term stability, and second-order convergence with the moderate time step restriction. Moreover, the adaptive DLN algorithms by the required error or numerical dissipation criterion are presented to balance the accuracy and computational cost. Numerical tests will be given to support the main conclusions.

Improved dissipativity‐based analysis and synthesis of T‐S fuzzy systems with aperiodic memory sampled‐data controllers via an augmented looped‐functional

AbstractThe dissipativity‐based analysis and synthesis issues of Takagi‐Sugeno (T‐S) fuzzy systems by applying aperiodic memory sampling control are investigated in this paper. Compared with the more conservative dissipative conditions and controller design methods proposed in the past based on Lyapunov theory, the main purpose of this paper is to obtain a less conservative dissipative criterion and devise an aperiodic memory sampled‐data controller. Firstly, the sampling controller is assumed to work in aperiodic sample mode, and the time delay in the communication network is considered. Next, an augmented delay‐product‐type looped‐functional is proposed such that the whole information of sampling and delay, which has not been studied before, is well taken into account. A new dissipative criterion and an aperiodic sampled‐data control strategy are proposed by applying free‐matrix‐based integral inequalities consequently. Finally, a truck‐trailer system is implemented to elaborate the availability and the merit of the designed strategy.

Generalized sliding event‐triggered control for dissipative performance of Markov switching dynamic systems

SummaryIn this paper, a generalized sliding event‐triggered control for the closed‐loop Markov switching systems (CLMSSs) is studied. It is proved that the system is driven to the designed sliding mode surface under a given sliding mode controller. A generalized sliding event‐triggered controller is developed to obtain strictly dissipative performance of CLMSSs, in which the combination of sliding mode control and event‐triggering protocol makes the control performance more efficient and generalized. Further, two dissipative criteria for CLMSSs are established. Finally, the results of numerical simulations give a witness for the effectiveness of the given theorems and methods.

Discrete-State Decomposition Technique of Dissipativity Analysis for Discrete-Time Singular Systems With Time-Varying Delays.

This article is concerned with the problem of dissipativity for discrete-time singular systems with time-varying delays. First, the discrete-state decomposition technique is proposed after performing the restricted equivalent transformation for singular systems. To reduce the use of decision variables, the state-decomposed Lyapunov function is established based on the decomposed state vectors. Second, to obtain the condition with less conservatism, the two zero-value equations, especially concerning difference subsystems and algebraic ones, the discrete Wirtinger-based inequality and the extended reciprocally convex inequality are employed to bound the forward difference of the Lyapunov function. Then, the less conservative dissipativity criteria with lower computational complexity are obtained. Finally, simulation results are provided to demonstrate the superiority of the proposed technique.

Quasi-Synchronization and Dissipativity Analysis for Fractional-Order Neural Networks with Time Delay

The objective of this research is to examine the global dissipativity and quasi-synchronization of fractional-order neural networks (FNNs). A global dissipativity criterion is established through the creation of an appropriate Lyapunov function, together with some fractional-order inequality techniques. Additionally, the issue of quasi-synchronization for drive-response FNNs is investigated using linear state feedback control. The study reveals the synchronization error converges to a bounded region by choosing an appropriate control parameter. Finally, the effectiveness of the obtained works are validated through three numerical examples.

Dissipativity analysis for Lur'e systems with two additive time‐varying delays via some novel Lyapunov–Krasovskii functionals

AbstractThe problem of dissipativity analysis is discussed for Lur'e systems with two additive time‐varying delays (ATDs) in this paper. Based on the dynamic delay interval (DDI) method, some novel Lyapunov‐Krasovskii functionals (LKFs) are constructed, in which part of Lyapunov matrices are requested to be positive definite. Then strictly dissipativity criteria of Lur'e systems with ATDs are presented in terms of linear matrix inequalities (LMIs). As by‐products, the stability criteria of Lur'e systems with ATDs and the systems with ATDs are derived. Finally, several numerical examples are used to illustrate the effectiveness and superiority of these criteria.

Further Results on Dissipativity Analysis for T–S Fuzzy Systems Based on Sampled-Data Control

This article investigates the dissipative stability and stabilization problems of Takagi–Sugeno fuzzy systems by employing sampled-data control. First, in order to enhance the adaptability of the controller, the internal and external influence factors, such as communication time delay and aperiodic sampling pattern, are taken into consideration in the design process. Then, some new terms are proposed to construct the looped-functional-like Lyapunov functional, which can improve the dissipative performance, enlarge the admissible upper bound of the aperiodic sampling periods, and reduce the occupation of control signals in the communication channel. Next, based on the free-matrix-based integral inequalities, some novel dissipative criteria are presented in terms of linear matrix inequalities. Finally, the superiority of the provided criteria is demonstrated through a truck–trailer system.

Asynchronous Sampled-Data Controller Design for Switched Markov Jump Systems and Its Applications

This article is dedicated to design asynchronous aperiodic sampled-data controller for a class of Markov jump systems with switching transition rate. The sampling controller corresponding switching transition rate matrix mode is not synchronized with the system corresponding switching transition rate matrix mode due to the possible switching of the transfer rate matrix in the sampling interval. With the help of T–S fuzzy models, the state-space representation of the system is turned into a fuzzy Itô stochastic switched Markov jump systems. By constructing novel Lyapunov functionals, mean square exponential stability criteria, and dissipativity criteria are presented. Furthermore, an asynchronous aperiodic sampled-data controller is designed for fuzzy Itô stochastic Markov jump systems. At last, by fuzzing the nonlinear tunnel diode circuit model and nonlinear mass-spring-damper mechanical model, the effectiveness and lower conservativeness of the proposed method are illustrated.

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>

Dissipative state observer design for nonlinear time-delay systems

This paper is concerned with the design of dissipative state observers for a family of time-delay nonlinear systems. The Dissipativity method, proposed by one of the authors for delay-free nonlinear systems, is extended here to a class of time-delay nonlinear systems. The design method consists in decomposing the time-delay estimation error dynamics into a time-delay linear subsystem and a time-varying memoryless nonlinearity, connected in a negative feedback loop. By using some storage functionals, both delay-independent and delay-dependent dissipativity criteria are derived in order to guarantee the exponential convergence property of the observer. The exponential stability of the estimation error is then ensured, assuming that the nonlinearity is dissipative with respect to a quadratic supply rate and the linear part is designed, through the observer gains, to be dissipative with respect to a complementary supply rate. The design conditions are formulated in terms of tractable bilinear (BMI’s) or linear matrix inequalities (LMI’s). An interesting advantage is that the proposed dissipative design extends and generalizes under a unified framework several methods available in the literature, since a wide diversity of nonlinearities can be considered. Numerical examples are provided to demonstrate the effectiveness of the theoretical results.

New insight into fracturing characterization of shale under cyclic soft stimulation: A lab-scale investigation

The cyclic soft stimulation (CSS) is a new method of reservoir reforming for which the mechanism of fracturing crack propagation is ambiguous with regard to the alternating fluid pressure. This study aims to provide a comprehensive understanding of the fracturing mechanical characterizations of CSS under different magnitudes and amplitudes of the alternating fluid pressure. Acoustic emission (AE) is recorded to investigate the damage evolution under CSS based on the b value analysis of AE. Experimental results reveal the difference of pressure in a crack under different cyclic fluid pressure conditions. The AE results show that the maximum radiated energy under CSS tends to be reduced with the increase in the amplitude and magnitude of the alternating fluid pressure. The finishing crucial touch is that the crack extending criterion under CSS is proposed, which combines the injection parameters, the rock properties and in-situ stress. According to the crack extending criterion, the fluctuation fluid pressure causes the reduction of a critical crack extending pressure, and the CSS causes the crack to initiate and propagate under low fluid pressure. Under a higher-value magnitude of alternating fluid pressure, the cyclic times of CSS is less for the crack initiation. In supplement to the crack extending criterion, a distinct relationship between the radiated energy and the cyclic fluid pressure also is established based on the energy dissipation criterion. These new findings provide an insight into the determination of crack extending criterion under CSS for efficiently implementing shale fracturing.

An Extended Dissipative Analysis of Fractional-Order Fuzzy Networked Control Systems

This study presents an extended dissipative analysis of fractional order fuzzy networked control system with uncertain parameters. First, we designed the network-based fuzzy controller for the considered model. Second, a novel Lyapunov-Krasovskii functional (LKF) approach, inequality techniques, and some sufficient conditions are established, which make the proposed system quadratically stable under the extended dissipative criteria. Subsequently, the resultant conditions are expressed with respect to linear matrix inequalities (LMIs). Meanwhile, the corresponding controller gains are designed under the larger sampling interval. Finally, two numerical examples are presented to illustrate the viability of the obtained criteria.

Event-Triggered Bipartite Consensus for Fuzzy Multiagent Systems Under Markovian Switching Signed Topology

In this article, we study the problems of bipartite and cooperative consensus with a strictly dissipative performance for fuzzy multiagent systems (MASs) in a unified framework. First, we prove that bipartite consensus over a structurally balanced signed graph is equivalent to cooperative consensus over the corresponding unsigned graph by leveraging the gauge transformation for a class of nonlinear MASs. Then, a polynomial fuzzy model is constructed to describe the nonlinear MAS formed by one leader and followers. For mitigating communication and computational load, a mode-dependent event-triggered transmission strategy is proposed. By establishing the switching topologies through Markovian process, a new sampled-data event-triggered consensus protocol is designed. With a mode-dependent Lyapunov–Krasovskii function, a novel relaxed dissipative criterion is obtained. The criterion guarantees that all agents can achieve both event-triggered cooperative consensus and event-triggered bipartite consensus with the same magnitude but opposite signs for MASs over structurally balanced signed directed graphs and Markovian switching topologies. Moreover, the event-triggered parameters and consensus control gains can be numerically solved via the sum-of-squares method. Simulation results are given to show the effectiveness of the proposed design method.

Novel Global Asymptotic Stability and Dissipativity Criteria of BAM Neural Networks With Delays

In this article, issues of both stability and dissipativity for a type of bidirectional associative memory (BAM) neural systems with time delays are investigated. By using generalized Halanay inequalities and constructing appropriate Lyapunov functionals, some novelty criteria are obtained for the asymptotic stability for BAM neural systems with time delays. Also, without assuming boundedness and differentiability for activation functions, some new sufficient conditions for proving the dissipativity are established by making use of matrix theory and inner product properties. The received conclusions extend and improve some previously known works on these problems for general BAM neural systems. In the end, numerical simulation examples are made to show the availability of the theoretical conclusions.

Investigation of physical aspects of energy dissipation in materials under static and dynamic loading

The research is carried out to determine the qualitative and quantitative picture of changes in energy scattering in specific materials and environments under different laws of their loading, processing and creation of new mixtures and materials. It was found that different methods are used to determine the dissipative characteristics, the assessment of which makes it difficult to assess the reliability of the results, as different assumptions and assumptions are accepted. The study of the physical aspects of energy scattering in materials and media is carried out according to linear and nonlinear load laws based on the use of hysteresis loop methods in transient and constant load regimes. It is found that the shape of the hysteresis loop depends to some extent on the law of change of load per cycle. The method of attenuating oscillations of energy absorption estimation by determining the logarithmic decrement of oscillations is used. According to the results of processing the measurement results, it is found that in the studies performed, the energy absorption coefficient varies in the range of 0.04-0.20, depending on the amplitude of relative deformation. which has elastically viscous properties and is under the action of force load. In physical terms, this formula determines the energy consumption per unit volume of material, takes into account the asymmetry of the load and can serve as an energy criterion for energy dissipation in materials under load.