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This paper studies the input-to-state stability (ISS) and uniform stability for impulsive nonlinear systems with delayed impulses, where delays are flexible between two consecutive impulsive instants. Illustrating effects caused by delays, concepts of generalised average impulsive delay and generalised reverse average impulsive delay are introduced, and more applicable in practice. Moreover, sufficient conditions for stability properties are formulated with destabilising and stabilising impulses through a general candidate ISS-Lyapunov function and the generalised conditions. It is shown that the double effects of delays in impulses (i.e. stabilising an initial unstable system, or contrarily, destabilising an initial stable system) coincide with the existing results using the exponential candidate ISS-Lyapunov function. Finally, two examples are provided to demonstrate our developed techniques. [ABSTRACT FROM AUTHOR]

This paper is devoted to achieving finite‐time and fixed‐time average consensus of nonlinear multi‐agent systems (NMASs). Different from the majority of finite‐time and fixed‐time controllers, a novel unified two‐phase control (UTPC) strategy is proposed to drive NMASs to achieve average consensus in finite/fixed time, which cleverly combines aperiodically intermittent impulsive control and unified feedback control. Furthermore, a pivotal lemma is put forward to provide guidance for selecting controller parameters and estimating the settling time. In the light of the developed control framework, meanwhile, several sufficient conditions are derived to guarantee that all agents can reach finite/fixed‐time average consensus. Finally, simulation results are presented to validate the effectiveness of our derived results. [ABSTRACT FROM AUTHOR]

This study aims to address the non-fragile exponential synchronisation problem of stochastic neural networks (SNNs). To cut down unnecessary control costs, a novel aperiodic intermittent-based impulsive control (APIIC) is designed in this investigation. Besides, the randomly occurring gain fluctuation (ROGF) is considered in APIIC, which satisfies certain Bernoulli distributed white noise sequences. By exploiting the Lyapunov approach and the average dwell-time technique, some sufficient criteria are derived in terms of linear matrix inequalities, which ensure that APIIC can achieve exponential synchronisation of SNNs with and without ROGF. More intriguingly, a technical definition of aperiodic window-based average impulsive interval is developed to cut back the conservativeness of these results. At last, the effectiveness of our explored results is confirmed by several numerical examples. [ABSTRACT FROM AUTHOR]

This paper focuses on the leader–follower quasi-consensus problem of multi-agent systems, considering the practical communication scenarios which involve packet loss. The phenomenon of packet loss is described in terms of the packet loss rate. A novel hybrid event-triggered impulsive control strategy is proposed, the Lyapunov stability theory is employed to derive sufficient conditions for realizing the leader–follower quasi-consensus, and the exclusion of Zeno behavior is demonstrated. Finally, a numerical simulation example is provided to verify the effectiveness of the proposed approach. The simulation results indicate that the packet loss rate is closely related to the control gain and the maximum triggered interval, specifically because as the packet loss rate increases, the trigger frequency also increases. [ABSTRACT FROM AUTHOR]

This paper investigates the exponential consensus problem for a class of nonlinear leader-following multi-agent systems using impulsive control, where impulses are generated by the event-triggered mechanism and are subjected to actuation delays. It is proved that Zeno behavior can be avoided, and by employing the linear matrix inequality technique, some sufficient conditions for realizing exponential consensus of the considered system are derived. Actuation delay is an important factor affecting the consensus of the system, and our results show that increasing the actuation delay can enlarge the lower bound of the triggering interval, while it harms the consensus. To demonstrate the validity of the obtained results, a numerical example is provided. [ABSTRACT FROM AUTHOR]

Lower limb rehabilitation exoskeleton robots (LLRERs) play an important role in lower limb rehabilitation training and assistance walking for patients with lower limb movement disorders. In order to reduce and eliminate adverse effects on the accuracy of human motion gait tracking during walking with an LLRER, which is caused by the gravity and friction, the periodic ground shock force, and the human–exoskeleton interaction force, this paper proposes a feedforward–feedback hybrid control strategy of sliding mode impulsive control with gravity and friction compensation, based on the event-triggered mechanism of Lyapunov function. Firstly, to realize high-precision gait tracking with bounded error, some constraints on controller parameters are deduced by analyzing the Lyapunov-based stability. Secondly, the Zeno behavior of impulsive event triggers is excluded by the analysis of three different cases of the triggering time sequence. Finally, the effectiveness of the proposed hybrid controller is verified by the numerical simulation of the LLRER human–exoskeleton integrated system based on a three-link simplified model. It shows that an event-triggered sliding mode impulsive control strategy with gravity and friction compensation can achieve complete gait tracking with bounded error and has excellent dynamic performance under the constraints. [ABSTRACT FROM AUTHOR]

This paper tackles the leader-following exponential consensus (LFEC) problem of nonlinear stochastic discrete-time multi-agent systems (DTMASs), which are subject to parameter uncertainties, stochastic disturbances and time-varying delay. An effective impulsive control strategy is utilised to guarantee that the leader-following consensus can be achieved exponentially. Particularly, several sufficient criteria regarding LFEC are derived by exploring the Lyapunov–Krasovskii functional and the linear matrix inequality technique. Additionally, the definition of the average impulsive interval is embedded into our developed results, which makes the results to be less conservative than those utilising the maximum and minimum impulsive intervals. At last, by the demonstration of numerical simulation results, the developed results are proven to be effective for achieving the LFEC of DTMASs. [ABSTRACT FROM AUTHOR]

In this paper, the consensus of fractional-order multi-agent systems is studied. By utilizing the unique properties of fractional-order calculus, namely hereditary and infinite memory, a new design scheme of the event-triggered pinning impulsive control strategy is proposed. Compared with the fixed pinning technique, the pinning agents here can be variable at each impulsive instant based on the considered two pinning rules (i.e., selecting randomly and according to the distances of error states). With the introduced rules, sufficient conditions are derived for consensus of systems, and the Zeno behavior is also excluded. Finally, our results show that the distance-ordered pinning can be achieved faster than the one with randomly pinning selection, and the inner impulsive gain of the impulsive controller can not be too large. [ABSTRACT FROM AUTHOR]

The quasi-consensus of a class of nonlinear time-varying multi-agent systems suffering from both external inputs and deception attacks is studied in this paper. This is different from a time-varying matrix, which is assumed to be bounded; further reasonable assumptions are supposed. In addition, impulsive deception attacks modeled with Bernoulli variables are considered. Sufficient conditions to achieve quasi-consensus are given, and the upper bounds of the error state related to the deception attacks is derived. Finally, a numerical simulation example is provided to show the validity of the obtained results. [ABSTRACT FROM AUTHOR]

This work is concerned with the finite‐time consensus of leader‐following non‐linear multi‐agent systems by means of distributed event‐triggered impulsive control. The finite‐time consensus protocol is first put forward based on event‐triggered impulsive strategies, where the impulsive instants are determined by the proposed event‐triggered condition. For the event‐triggered condition, it not only determines the impulsive instants but also effects the update time of the finite‐time control. Moreover, compared with the existing finite‐time controllers, the controller designed in this work does not contain any sign function, thereby overcoming the chattering phenomenon. In addition, without finding Zeno behaviour, the feasibility of the proposed control protocol is demonstrated. Lastly, simulations are employed to demonstrate the effectiveness of the proposed control schemes. [ABSTRACT FROM AUTHOR]

In order to bring the theoretical results into harmony or agreement with the reality, this paper copes with the leader-following mean square consensus issue for a class of nonlinear stochastic multi-agent systems with randomly occurring nonlinearities (RONs) and randomly occurring uncertainties (ROUs) under impulse time windows (ITWs). As a majorizing preconfigured mechanism of the windows, the configuration named periodically variable impulse time windows (PVITWs) is put forward. It not only ensures the periodic-based layout of impulse time window (ITW), but also allows the position and width of the window to be arbitrarily adjustable, so that the preset of ITW is more suitable for applications. Based on the Lyapunov stability theory and graph theory, the corresponding sufficient mean square consensus criteria are given. Finally, the feasibility of theoretical analysis is illustrated by numerical simulations. [ABSTRACT FROM AUTHOR]

Summary: In this article, we are concerned with the problem on input‐to‐state stability (ISS) for discrete‐time time‐varying switched delayed systems. Some Krasovskii and Razumikhin ISS criteria are provided by using the notions of uniformly asymptotically stable (UAS) function and mode‐dependent average dwell time (MDADT). With the help of the concept of UAS function, the advantage of our results in this article is that the coefficients of the first‐order difference inequalities for the mode‐dependent Krasovskii functionals and mode‐dependent Razumikhin functions are allowed to be time‐varying, mode‐dependent, and can even take both positive and negative values, and the whole switched system can be allowed to have both ISS subsystems and non‐ISS subsystems. With the aid of the notion of MDADT, each subsystem can have its own average dwell time. As an application, we also provide an ISS criterion for discrete‐time time‐varying switched delayed Hopfield neural networks with disturbance inputs. Numerical simulations verify the effectiveness of the established criteria. [ABSTRACT FROM AUTHOR]

This study investigates the problem of input‐to‐state stability (ISS) and integral input‐to‐state stability (iISS) of impulsive time‐varying delayed systems. Some Lyapunov–Krasovskii‐type criteria on ISS and iISS which are effective for destabilising impulses and stabilising impulses are derived from advanced linear dissipation inequalities under average impulsive interval constraints. The conditions which require the coefficients of the linear dissipation inequalities on the Lyapunov–Krasovskii functionals to be constants in the existing results on ISS/iISS of impulsive delayed systems are weakened. In this study, with the aid of the notions of uniformly exponentially stable function and average impulsive interval, the results allow the coefficients of the developed linear dissipation inequalities on the Lyapunov–Krasovskii functionals to be time‐varying functions which can take both positive and negative values, and the impulsive intervals of an impulsive sequence are allowed to have arbitrarily small lower bound and enough big upper bound simultaneously. Two examples are presented to illustrate the effectiveness of the results. [ABSTRACT FROM AUTHOR]

This paper discusses the problem of input-to-state stability (ISS) of time-varying impulsive delayed systems. By introducing a switching parameter and using the notion of average impulsive interval, a unified Razumikhin-type criterion on ISS which is simultaneously effective for stabilizing impulses and destabilizing impulses is derived. The condition which requires the coefficient of the estimated upper bound of the derivative of a Lyapunov function to be constant in the existing results on ISS of impulsive systems is weakened. The results in this paper allow the coefficient of the derivative of a Lyapunov function to be time-varying function which can be both positive and negative and may even be unbounded. Furthermore, the impulsive intervals of an impulsive sequence are allowed to have arbitrarily small lower bound and large enough upper bound simultaneously. As a by-product, a unified criterion on ISS for time-varying impulsive delay-free systems is also presented. Two examples are presented to illustrate the effectiveness of our results. [ABSTRACT FROM AUTHOR]

This paper focuses on the leader-following consensus problem of nonlinear multi-agent systems with randomly occurring uncertainties and stochastic disturbances under impulsive control input. Based on the average impulsive interval, a unified consensus criterion is derived for multi-agent systems. On the other hand, our consensus criterion is applicable to impulsive control sequences in which the lower bound of impulsive interval is allowed to be arbitrarily small and the upper bound of impulsive interval is allowed to be big enough. The proposed consensus criterion is theoretically and numerically proved to be less conservative than existing results. Two numerical simulations illustrate the effectiveness of theoretical results. [ABSTRACT FROM AUTHOR]

• Integrating the advantages of intermittent control and impulsive control, a novel periodically intermittent impulsive control (PIIC) scheme is proposed to address the exponential leader-following consensus problem of stochastic discrete multi-agent systems (SDMASs) with and without DoS attacks, where the impulsive effect is available at the control windows only. In addition, comparing with the previous works, the discrete-time dynamics studied in this article is more comprehensive, which takes into account nonlinearities, parameter uncertainties, stochastic disturbances and DoS attacks. • For SDMASs without DoS attacks, we derive the relation among the control period, the control width and the impulsive interval via utilizing the Lyapunov method and the linear matrix inequality technique. In addition, for SDMASs with DoS attacks, we derive the control rate associated with the impulsive interval, the impulsive gain, the DoS attack ratio and the attack intensity under reasonable assumption that adversaries fail to work persistently within given intervals. • Motivated by the notion of average impulsive interval, a novel concept of periodic window-based average impulsive interval is presented to make our developed results less conservative, which can avoid employing the maximum and minimum impulsive intervals. This article is devoted to investigating the exponential leader-following consensus (ELFC) of stochastic discrete multi-agent systems (SDMASs) in the presence of parameter uncertainties, nonlinearities, stochastic disturbances and denial-of-service (DoS) attacks. A novel control strategy, namely, periodically intermittent impulsive control (PIIC), is designed to cut down unnecessary communication costs and maintain the well-pleasing performance, where the impulsive instants only appear at control windows. Specifically, we explore the ELFC of SDMASs without DoS attacks via the PIIC strategy. The relation among the control period, the control width and the impulsive interval is derived by mean of utilizing the Lyapunov method and the linear matrix inequality technique. Besides, for SDMASs under DoS attacks, the following results are obtained: 1) under reasonable assumption that adversaries fail to work persistently within given intervals, a sufficient criterion is derived to ensure the ELFC of SDMASs; 2) the control rate is derived associated with the impulsive interval, the impulsive gain, the DoS attack ratio and the attack intensity; and 3) the novel protocol can achieve ELFC and cut down control costs effectively. More interestingly, a novel concept of periodic window-based average impulsive interval is proposed to make our developed criteria less conservative. Finally, simulation examples are demonstrated to certify the applicability of PIIC and the effectiveness of our main results. [ABSTRACT FROM AUTHOR]

It is to study the strong convergence of a composite iteration process to a common fixed point for two nonexpansive semigroups, which is a solution of certain variational inequality under certain conditions. The results of this article extend the corresponding recent results by some others. [ABSTRACT FROM AUTHOR]

Abstract: Bidirectional associative memory (BAM) model is considered with the introduction of continuously distributed delays in the leakage (or forgetting) terms. By using continuation theorem in coincidence degree theory and the Lyapunov functional, some very verifiable and practical algebraic mean delay dependent criteria on the existence and global attractive periodic solutions are derived. [Copyright &y& Elsevier]

Abstract: By using the generalized Borsuk theorem in coincidence degree theory, some criteria for guaranteeing the existence of -periodic solutions for a Rayleigh system of -Laplacian type are derived. [Copyright &y& Elsevier]

Abstract: By using topological degree theory and some analytical skill, some criteria to guarantee the existence of -periodic solutions are derived for -Laplacian neutral Rayleigh equation with a deviating argument of the following form [Copyright &y& Elsevier]

Abstract: By using the generalized Borsuk theorem in coincidence degree theory, some new criteria for guaranteeing the existence of -periodic solutions for -Laplacian Rayleigh equations with a deviating argument are derived. [Copyright &y& Elsevier]

Abstract: By using generalized Borsuk theorem in coincidence degree theory, some criteria to guarantee the existence of ω-periodic solutions for a class of p-Laplacian system are derived. [Copyright &y& Elsevier]

This paper discusses the existence and multiplicity of positive solutions for the following first order periodic boundary value problemBy utilizing a fixed point theorem on cone, some existence and multiplicity results of positive solutions are derived. [Copyright &y& Elsevier]

In this paper, we investigate the finite-time synchronization problem for a class of Markovian jumping complex networks (MJCNs) with non-identical nodes and impulsive effects. Sufficient conditions for the MJCNs are presented based on an M-matrix technique, Lyapunov function method, stochastic analysis technique, and suitable comparison systems to guarantee finite-time synchronization. At last, numerical examples are exploited to illustrate our theoretical results, and they testify the effectiveness of our results for complex dynamic systems. [ABSTRACT FROM AUTHOR]

5-Hydroxytryptophan (5-HTP), as the precursor of serotonin and melatonin in animals, can regulate mood, sleep, and behavior, which is widely used in pharmaceutical and health products industry. The enzymatic production of 5-hydroxytryptophan (5-HTP) from L-tryptophan (L-Trp) using tryptophan hydroxylase (TPH) show huge potential in application due to its advantages, such as mild reaction conditions, avoidance of protection/deprotection processes, excellent regioselectivity and considerable catalytic efficiency, compared with chemical synthesis and natural extraction. However, the low thermostability of TPH restricted its hydroxylation efficiency toward L-Trp. In this study, we aimed to improve the thermostability of TPH via semi-rational design guided by (folding free energy) ΔΔG fold calculation. After two rounds of evolution, two beneficial mutants M1 (S422V) and M30 (V275L/I412K) were obtained. Thermostability evaluation showed that M1 and M30 possessed 5.66-fold and 6.32-fold half-lives (t 1/2) at 37 °C, and 4.2 °C and 6.0 °C higher melting temperature (T m) than the WT, respectively. The mechanism behind thermostability improvement was elucidated with molecular dynamics simulation. Furthermore, biotransformation of 5-HTP from L-Trp was performed, M1 and M30 displayed 1.80-fold and 2.30-fold than that of WT, respectively. This work provides important insights into the thermostability enhancement of TPH and generate key mutants that could be robust candidates for practical production of 5-HTP. [ABSTRACT FROM AUTHOR]

Abstract: A demiclosed principle is proved for asymptotically nonexpansive mappings in the intermediate sense. Moreover, it is proved that the modified three-step iterative sequence converges weakly and strongly to common fixed points of three asymptotically nonexpansive mappings in the intermediate sense under certain conditions. The results of this paper improve and extend the corresponding results of [M.O. Osilike, S.C. Aniagbosor, Weak and strong convergence theorems for fixed points of asymptotically nonexpansive mappings, Math. Comput. Modelling 32 (2000) 1181–1191; G.E. Kim, T.H. Kim, Mann and Ishikawa iterations with errors for non-Lipschitzian mappings in Banach spaces, Comput. Math. Appl. 42 (2001) 1565–1570; B.L. Xu, M.A. Noor, Fixed point iterations for asymptotically nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 267 (2002) 444–453; K. Nammanee, S. Suantai, The modified Noor iterations with errors for non-Lipschitzian mappings in Banach spaces, Appl. Math. Comput. 187 (2007) 669–679; K. Nammanee, M.A. Noor, S. Suantai, Convergence criteria of modified Noor iterations with errors for asymptotically nonexpansive mappings, J. Math. Anal. Appl. 314 (2006) 320–334] and other corresponding known ones. On the other hand, we show the necessary and sufficient condition for the strong convergence of the modified three-step iterative sequence to some common fixed points of . [Copyright &y& Elsevier]

This paper establishes the asymptotic closed forms of the expectation and variance of the Pearson׳s rank-variate correlation coefficient (PRVCC) with respect to samples drawn from bivariate normal populations. The variance-stability features of Fisher׳s z -transform on PRVCC is also investigated under normal assumptions. To gain deeper insight into PRVCC, we further compare PRVCC to other two closely related correlation coefficients, namely, Pearson׳s product moment correlation coefficient (PPMCC) and Gini correlation (GC). Theoretical and simulation results reveal the advantages of PRVCC over PPMCC and/or GC in terms of mathematical tractability and smaller mean square error (MSE) under different circumstances. The newly found theoretical results along with other desirable properties enable PRVCC to be a useful alternative to the existing coefficients, especially when the samples follow distributions whose tails are heavier than that of normal distribution. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the nonlinear boundary value problem is studied. By using the fixed point index theory, some existence, multiplicity, and nonexistence results for positive solutions are derived in terms of different values of . The results obtained herein generalize and improve the main results of [J.R. Graef, L. Kong, H. Wang, Existence, multiplicity, and dependence on a parameter for a periodic boundary value problem, J. Differential Equations 245 (2008) 1185–1197; X. Hao, L. Liu, Y. Wu, Existence and multiplicity results for nonlinear periodic boundary value problems, Nonlinear Anal. 72 (2010) 3635–3642] and some other known results. [Copyright &y& Elsevier]