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In this research, the three-dimensional (3D) steady and incompressible laminar Homann stagnation point nanofluid flow over a porous moving surface is addressed. The disturbance in the porous medium has been characterized by the Darcy-Forchheimer relation. The slip for viscous fluid is considered. The energy equation is organized in view of radiative heat flux which plays an important role in the heat transfer rate. The governing flow expressions are first altered into first-order ordinary ones and then solved numerically by the shooting method. Dual solutions are obtained for the velocity, skin friction coefficient, temperature, and Nusselt number subject to sundry flow parameters, magnetic parameter, Darcy-Forchheimer number, thermal radiation parameter, suction parameter, and dimensionless slip parameter. In this research, the main consideration is given to the engineering interest like skin friction coefficient (velocity gradient or surface drag force) and Nusselt number (temperature gradient or heat transfer rate) and discussed numerically through tables. In conclusion, it is noticed from the stability results that the upper branch solution (UBS) is more reliable and physically stable than the lower branch solution (LBS). [ABSTRACT FROM AUTHOR]

This article studies the generalized (2 + 1)-dimensional shallow water equation by applying two recent analytical schemes (the extended simplest equation method and the modified Kudryashov method) for constructing abundant novel solitary wave solutions. These solutions describe the bidirectional propagating water wave surface. Some obtained solutions are sketched in two- and three-dimensional and contour plots for demonstrating the dynamical behavior of these waves along shallow water. The accuracy of the obtained solutions and employed analytical schemes is investigated using the evaluated solutions to calculate the initial condition, and then the well-known variational iterational (VI) method is applied. The VI method is one of the most accurate semi-analytical solutions, and it can be applied for high derivative order. The used schemes' performance shows their effectiveness and power and their ability to handle many nonlinear evolution equations. [ABSTRACT FROM AUTHOR]

Abstract: In this article, we show the existence of intertwined basins of attraction for a class of prey–predator systems, which improves the extant results by deleting some crucial and hard testing conditions. [Copyright &y& Elsevier]

Abstract: In this paper, the authors show a relation between the generalized convexity and super- (sub-)multiplicative property, and discuss some generalized convexity and inequalities involving the Gaussian hypergeometric function, the generalized η-distortion function and the generalized Grötzsch function . [Copyright &y& Elsevier]

This paper deals with space Beltrami system with three characteristic matrices in even dimensions, which can be regarded as a generalization of space Beltrami system with one and two characteristic matrices. It is transformed into a nonhomogeneous p-harmonic equation d*A(x, dfI ) = d*B(x,Df) by using the technique of outer differential forms and exterior algebra of matrices. In the process, we only use the uniformly elliptic condition with respect to the characteristic matrices. The Lipschitz type condition, the monotonicity condition and the homogeneous condition of the operator A and the controlled growth condition of the operator B are derived. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we prove that the inner and outer linearly locally connected sets of are invariant respectively under quasiconformal mappings which fixed the point at infinity. On the other hand, we prove the converses of above results to be true also. [Copyright &y& Elsevier]

Abstract: A stable set of a graph is a vertex set in which any two vertices are not adjacent. It was proven in [A. Brandstädt, V.B. Le, T. Szymczak, The complexity of some problems related to graph 3-colorability, Discrete Appl. Math. 89 (1998) 59–73] that the following problem is NP-complete: Given a bipartite graph G, check whether G has a stable set S such that is a tree. In this paper we prove the following problem is polynomially solvable: Given a graph G with maximum degree 3 and containing no vertices of degree 2, check whether G has a stable set S such that is a tree. Thus we partly answer a question posed by the authors in the above paper. Moreover, we give some structural characterizations for a graph G with maximum degree 3 that has a stable set S such that is a tree. [Copyright &y& Elsevier]

Abstract: This Letter provides new sufficient conditions for the existence, uniqueness and global exponential stability of the equilibrium point of recurrent neural networks with time-varying delays by employing Lyapunov functions and using the Halanay inequality. The time-varying delays are not necessarily differentiable. Both Lipschitz continuous activation functions and monotone nondecreasing activation functions are considered. The derived stability criteria are expressed in terms of linear matrix inequalities (LMIs), which can be checked easily by resorting to recently developed algorithms solving LMIs. Furthermore, the proposed stability results are less conservative than some previous ones in the literature, which is demonstrated via some numerical examples. [Copyright &y& Elsevier]

This work examines the entropy generation with heat and mass transfer in magnetohydrodynamic (MHD) stagnation point flow across a stretchable surface. The heat transport process is investigated with respect to the viscous dissipation and thermal radiation, whereas the mass transport is observed under the influence of a chemical reaction. The irreversibe factor is measured through the application of the second law of thermodynamics. The established non-linear partial differential equations (PDEs) have been replaced by acceptable ordinary differential equations (ODEs), which are solved numerically via the bvp4c method (built-in package in MATLAB). The numerical analysis of the resulting ODEs is carried out on the different flow parameters, and their effects on the rate of heat transport, friction drag, concentration, and the entropy generation are considered. It is determined that the concentration estimation and the Sherwood number reduce and enhance for higher values of the chemical reaction parameter and the Schmidt number, although the rate of heat transport is increased for the Eckert number and heat generation/absorption parameter, respectively. The entropy generation augments with boosting values of the Brinkman number, and decays with escalating values of both the radiation parameter and the Weissenberg number. [ABSTRACT FROM AUTHOR]

• Design fixed-time adaptive chattering-free controllers. • Propose fixed-time synchronization adaptive chattering-free control strategy for different types of networks. • Construct double-layered multi-weighted coupling networks. • Configure complex networks with linear coupling. • The fixed time is related to the designed controllers, node sizes of networks and dimension of nodes. The problem for fixed-time outer synchronization of double-layered multi-weighted coupled complex networks with stochastic effects is considered in this paper. To suppress chattering in synchronization, an adaptive chattering-free control algorithm is designed. Based upon the Lyapunov stability theory, some sufficient criteria for the adaptive stochastic outer synchronization are proposed. The designed adaptive chattering-free controller and the sufficient conditions can be applicable to not only the fixed-time stochastic synchronization of double-layered multi-weighed undirected networks, but also the fixed-time stochastic synchronization of double-layered multi-weighted directed networks. Our theoretical results indicate that the settling time is related to the size of dynamic networks, the dimension of each node and the designed adaptive controllers in the fixed-time stochastic outer synchronization. The effectiveness of our derived theoretical framework is illustrated via simulation examples. [ABSTRACT FROM AUTHOR]

In this paper, to resist stochastic cyber attacks and suppress the influence of the exogenous disturbance in synchronization of multiplex neural networks, an adaptive quantization control strategy is proposed. To overcome uncertainties and represent constraints in communication, an adaptive quantitative controller is designed, which is used to arrive outer synchronized behavior with an H ∞ performance between the multiplex neural networks under stochastic cyber attacks and exogenous disturbance. The node of the multiplex networks is neural networks which is named neural sub-networks. It is assumed that the neural sub-networks in the multiplex networks with delay topology are coupled by nonlinear functions. Based on Lyapunov stability method, the conditions for the multiplex networks to achieve synchronization with an H ∞ performance are presented. Finally, numerical example illustrates the effective of the theoretical framework. [ABSTRACT FROM AUTHOR]

Abstract: In this work the authors present some new lower and upper bounds for the functions and , thus improving some inequalities put forward by Klén et al. (2010) in the paper . [Copyright &y& Elsevier]

The synchronization problem is considered for a class of stochastic complex networks with interval time-varying delays. Based on the Lyapunov functional method and stochastic analysis theory, delay-dependent sufficient conditions are obtained, which ensure that the identical delayed networks are globally synchronized in the mean square sense. Furthermore, the 'piecewise delay' approach is improved to deal with the synchronization problem of systems with stochastic disturbances by introducing two new lemmas. The efficiency and applicability of the proposed methodology are demonstrated by two numerical examples. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the problems of robust global exponential synchronization for a class of complex networks with time-varying delayed couplings are considered. Each node in the network is composed of a class of delayed neural networks described by a nonlinear delay differential equation of neutral-type. Since model errors commonly exist in practical applications, the parameter uncertainties are involved in the considered model. Sufficient conditions that ensure the complex networks to be robustly globally exponentially synchronized are obtained by using the Lyapunov functional method and some properties of Kronecker product. An illustrative example is presented to show the effectiveness of the proposed approach. [Copyright &y& Elsevier]

Local regularity and local boundedness results for very weak solutions of obstacle problems of the A-harmonic equation divA(x,∇u(x)) = 0 are obtained by using the theory of Hodge decomposition, where ∣A(x, ξ)∣ ≈ ∣ξ∣p-1. [ABSTRACT FROM AUTHOR]

Abstract: In this note we investigate the convexity of zero-balanced hypergeometric functions with respect to Hölder mean. [Copyright &y& Elsevier]

Abstract: In this paper, the authors study monotonicity and convexity of the generalized elliptic integrals and certain combinations of these special functions, such as and . Making use of these results, the authors obtain some sharp inequalities for the so-called Ramanujan''s generalized modular functions. [Copyright &y& Elsevier]

In this paper, we first define a new kind of two-weight-Arλ3 (λ1, λ2, Ω)-weight, and then prove the imbedding inequalities for A-harmonic tensors. These results can be used to study the weighted norms of the homotopy operator T from the Banach space Lp(D,Λl) to the Sobolev space W1,p(D,Λl-1), l = 1, 2, …, n, and to establish the basic weighted Lp-estimates for A-harmonic tensors. [ABSTRACT FROM AUTHOR]

Abstract: The authors prove a conjecture on elliptic integrals and obtain sharp bounds for and . By using Teichmüller''s module theorem, the authors obtain a distortion theorem of K-quasiconformal mappings on the plane. [Copyright &y& Elsevier]

Abstract: This paper investigates the problems of robust stochastic stabilization and robust control for uncertain neutral stochastic time-delay systems with time-varying norm-bounded parameter uncertainties appearing in both the state and input matrices. The time delay is assumed to be unknown. Sufficient conditions for the existence of state feedback controllers are proposed, which ensure mean-square asymptotic stability of the resulting closed-loop system and reduce the effect of the disturbance input on the controlled output to a prescribed level for all admissible uncertainties. A linear matrix inequality approach is employed to design the desired state feedback controllers. Furthermore, in the case when time delays appear in both the state and control input, results on the robust stochastic stabilization and robust control are also presented. An illustrative example is provided to show the potential of the proposed techniques. [Copyright &y& Elsevier]

In this article, we study the reachable set estimation and controller design problems for a class of discrete time‐varying‐delay singularly perturbed systems. First, by constructing a ε‐dependent Lyapunov–Krasovskii functional and using reciprocally convex inequality, delay‐dependent conditions are obtained to ensure the state of the system under zero initial conditions is contained by an ellipsoid for any singularly perturbed parameters below a given threshold. Second, by the method of designing a state‐feedback controller, sufficient conditions that the reachable set of the closed‐loop system can be included in a given ellipsoid are obtained for admissible singularly perturbed parameters. Finally, two examples are given to illustrate the effectiveness of the results. [ABSTRACT FROM AUTHOR]

This paper addresses the finite-time state estimation problem for semi-Markovian jump neural networks with sensor nonlinearities under the consideration of leakage delay and time-varying delay. The modes of original system and desired estimator are supposed to be asynchronous. Some sufficient conditions are proposed to guarantee the finite-time boundedness as well as mixed H ∞ and passive performance of the error system in terms of constructing Lyapunov–Krasovskii functionals. By utilizing affine Bessel-Legendre inequalities, a less conservative result can be achieved. By virtue of linear matrices inequalities approach, the asynchronous state estimator gains are obtained. Two numerical examples are provided to demonstrate the less conservativeness and effectiveness of our method. [ABSTRACT FROM AUTHOR]

The unavailability of wasted energy due to the irreversibility in the process is called the entropy generation. An irreversible process is a process in which the entropy of the system is increased. The second law of thermodynamics is used to define whether the given system is reversible or irreversible. Here, our focus is how to reduce the entropy of the system and maximize the capability of the system. There are many methods for maximizing the capacity of heat transport. The constant pressure gradient or motion of the wall can be used to increase the heat transfer rate and minimize the entropy. The objective of this study is to analyze the heat and mass transfer of an Eyring-Powell fluid in a porous channel. For this, we choose two different fluid models, namely, the plane and generalized Couette flows. The flow is generated in the channel due to a pressure gradient or with the moving of the upper lid. The present analysis shows the effects of the fluid parameters on the velocity, the temperature, the entropy generation, and the Bejan number. The nonlinear boundary value problem of the flow problem is solved with the help of the regular perturbation method. To validate the perturbation solution, a numerical solution is also obtained with the help of the built-in command NDSolve of MATHEMATICA 11.0. The velocity profile shows the shear thickening behavior via first-order Eyring-Powell parameters. It is also observed that the profile of the Bejan number has a decreasing trend against the Brinkman number. When ηi → 0 (i = 1, 2, 3), the Eyring-Powell fluid is transformed into a Newtonian fluid. [ABSTRACT FROM AUTHOR]

First, we consider a new Simpson's identity. This identity investigates our main results that consist of some integral inequalities of Simpson's type for the s –convex functions. From our main results, we obtain some special cases which are discussed in detail. Finally, some applications on the Bessel functions, special means of distinct positive real numbers, and error estimation about Simpson quadrature formula are presented to support our theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of event triggering H ∞ synchronization control for discrete-time switched complex networks via quasi-time asynchronous controllers. One event triggering mechanism is introduced with the triggering parameters depending on triggering states. Applying quasi-time dependent multiple Lyapunov functions and the mode-dependent average dwell time technique, quasi-time dependent synchronization conditions are obtained with a lower weighted performance index. And then, a quasi-time dependent asynchronous controller is designed with quasi-time dependent control gains in each triggering interval. In addition, not only no more than one switching, but also multiple switchings are taken into account in each triggering interval, by which the assumption in some existing results is relaxed. Finally, the proposed result is applied to the PWM-driven boost converter. [ABSTRACT FROM AUTHOR]

This paper discusses a neural dynamic surface control (DSC) problem for a class of nonlinear systems in the case of full-state constraints and unknown disturbances. Incorporating an improved DSC method and the neural networks (NNs) approximation with the minimization parameter method, an improved neural DSC approach is constructed for the studied system. By introducing a novel barrier Lyapunov function (BLF) in the design steps, the issue of full-state constraints existing in the system can be solved. The highlighting features of the proposed control method are that only one online estimation parameter should be updated, and the same stability property as the conventional backstepping method can be reserved. The transgressions of full state constraints never occur in the case of disturbances. By the Lyapunov stability analysis, all the signals of the closed-loop system are ultimately bounded. Finally, two simulation examples display the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

The saturation input control problem of discrete-time networked systems via adaptive event-triggered communication scheme is discussed in this paper. The criteria are derived by utilising a new Lyapunov functional to guarantee that the considered networked system with randomly occurring infinite distributed delays, random packet losses and sensor saturation is exponentially stable in mean square sense. A novel adaptive event-triggered law is proposed, which is dependent on the exponentially stable index α. The effectiveness of our proposed method is illustrated by both theoretical analysis and numerical simulations. [ABSTRACT FROM AUTHOR]

Sampled‐data based quantisation control for Takagi–Sugeno (T–S) fuzzy switched systems with actuator failures under asynchronous switching is studied. By the T–S fuzzy model, sampled‐data based asynchronous control is extended into switched non‐linear systems. An improved functional method is introduced. Applying this method, improved Lyapunov functionals are constructed. These functionals are mode dependent and piecewise continuous; not every term of these functionals is required to be positive definite; sampling states at both sides of sampling intervals are introduced into these functionals. More useful information with respect to system states is reflected in constructing functionals. Combining these functionals with the averaged dwell time technique, stabilisation conditions are relaxed, and improved exponential stabilisation criteria are obtained with less conservatism. In addition, variation ranges of membership functions are taken into account to reduce conservatism. Then, a sampled‐data based fuzzy quantisation controller is designed. Simulation examples are given to illustrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

In this paper, a partially mode-dependent dissipative filter design method is presented for uncertain Markovian jump systems with mixed delays and unknown transition rates. The uncertainty is assumed to be time-invariant which belongs to a ploytope. By constructing a mode-dependent and parameter-dependent Lyapunov–Krasovskii functional based on delay-partitioning approach, we propose a sufficient condition for the existence of a partially mode-dependent dissipative filter, which ensures that the resulting filtering error system is stochastically stable and dissipative. The filter parameters can be derived by using feasible solutions to a certain set of linear matrix inequalities. Finally, two simulation examples are provided to illustrate the effectiveness of the filter design technique. [ABSTRACT FROM AUTHOR]

This paper presents a novel robust adaptive neural control scheme which can be taken as a robustification of the adaptive backstepping design. The considered class of uncertainties contains unknown non-symmetric dead-zone inputs, time-varying delay uncertainties, unknown dynamic disturbances and unmodelled dynamics. The radial basis function neural networks (RBFNNs) are employed to approximate the unknown nonlinear functions obtained by Young’s inequality. By constructing exponential Lyapunov-Krasovskii functionals, the upper bound functions of the time-varying delay uncertainties are compensated for. Using Young’s inequality and RBFNNs, the assumptions with respect to unmodelled dynamics are relaxed. It is demonstrated that the proposed controller guarantees that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error eventually converges to a neighbourhood of zero. [ABSTRACT FROM AUTHOR]

This paper revisits the robust stabilization issue for uncertain singular Markovian jump systems (USMJSs) via dynamic-output-feedback (DOF) control. By establishing a new Lyapunov–Krasovskii functional with state decomposition components, some sufficient mean-square exponentially (MSE) admissible conditions (such as non-impulsiveness, regularity, and MSE stability) are obtained for the unforced nominal USMJS with time-varying delays. Then, based on the established criteria, the robust MSE admissibility of the USMJS is explored. Further, a DOF controller for the closed-loop USMJS is designed. Via applying a state decomposition recombination approach, a robust MSE stabilization criterion utilizing linear matrix inequality is derived. Meanwhile, by solving each decomposition component of the DOF controller, the desired DOF controller can be accurately determined. Finally, using two numerical examples, the superiority and feasibility of our method are demonstrated. [ABSTRACT FROM AUTHOR]

This paper considers the problem of global asymptotic regulation via output feedback for a class of uncertain feedforward nonlinear systems with input and state delays, where the bounds of time delays are unknown. With the help of the high-gain scaling approach and the idea of universal adaptive control, we explicitly construct an adaptive output compensator with a novel positive dynamic gain which compensates simultaneously the unknown delays and the output growth rate with unknown constant. Based on such output compensator, we reduce the conservatism of the restrictive conditions imposed on nonlinearities to generalise the existing results. By the Lyapunov–Krasovskii theorem, a delay-independent controller design scheme is proposed to guarantee that all the closed-loop signals are globally bounded while rendering the states of original system and the estimate states to globally asymptotically converge to zero. Finally, two illustrative examples are given to show the usefulness of the proposed design method. [ABSTRACT FROM PUBLISHER]

The problem of H∞ deconvolution filter design for a class of singular Markovian jump systems with time-varying delays and parameter uncertainties is considered in this paper. By constructing a more comprehensive stochastic Lyapunov-Krasovskii functional, novel delay-dependent conditions are established to guarantee the filtering error system is not only stochastically admissible, but also satisfies a prescribed H∞-norm level for all admissible uncertainties. The desired filter parameters can be obtained by solving a set of strict linear matrix inequalities. Two examples and an electrical RLC circuit example are employed to verify the effectiveness and usefulness of the proposed methods in the paper. [ABSTRACT FROM AUTHOR]

This study addresses the consensus problem of multi‐agent systems by combining adaptive control protocol and event‐triggered communication strategy. Two adaptive protocols are designed to guarantee the consensus. The event‐triggered communication strategy is utilised to save communication and reduce channel occupation. Each agent in the system sends its state to neighbours only at some irregular event instants determined by an appropriately designed event‐triggering condition. At first, the distributed event‐triggering condition of an agent only employs the state of its own and the state of the neighbours at their latest event instants. Later, another event‐triggering condition is given such that no global parameter is required for agents, such as the maximum eigenvalue of the Laplacian matrix. It is proven that the system can reach consensus by utilising the proposed control method. Illustrative examples are given to show the effectiveness of the control strategy. [ABSTRACT FROM AUTHOR]

In this paper, the problem of adaptive decentralized neural network (NN) control for a class of large-scale stochastic nonlinear time-delay systems with unknown dead-zone inputs is investigated. Neural networks are utilized to approximate unknown nonlinear functions, and an adaptive decentralized controller is constructed by incorporating the minimal learning parameters algorithm into backstepping design procedure. It is proved that the proposed control scheme guarantees that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded in probability. Finally, a numerical example is provided to demonstrate the effectiveness of the present results. [ABSTRACT FROM AUTHOR]

In this study, the problem of fault detection for a class of discrete‐time non‐linear networked control systems is investigated. An event modelled as a Markov chain taking matrix values in a certain set with partially known transition probabilities is utilised to characterise the phenomenon of the sensors assignment. A full‐order mode‐dependent fault detection filter is constructed and the corresponding fault detection problem is converted into an H∞ filtering problem of a Markov jump system with partially known transition probabilities. Sufficient conditions for the existence of the fault detection filter are formulated as a linear matrix inequality‐based convex optimisation problem. If the convex optimisation problem has a feasible solution, the corresponding fault detection filter parameters are determined. A numerical example with four cases of transition probability matrices is presented to show the usefulness of the developed method. [ABSTRACT FROM AUTHOR]