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This paper addresses the secure impulsive consensus tracking problem of Lipschitz nonlinear multi-agent systems in the presence of network-induced delays and discrete-time deception attacks in the controller-to-actuator channels. The information exchanges among agents are assumed to occur only at discrete instants satisfying a ranged dwell-time condition, and the occurrences of the deception attacks are governed by a set of Bernoulli processes. The tracking performance is characterized by the mean-square exponential input-state stability (MSEISS) of the tracking error system with delayed impulses and bounded disturbances, in which the MSEISS-gain is used to quantify the capacity of the distributed impulsive controllers against deception attacks. By modelling the impulse delays as the impulse intervals of the augmented tracking error system, the effect of impulse delays on MSEISS is captured by a switching-based discretized discontinuous weighted Lyapunov function. An impulse-delay-dependent criterion for the synthesis of a distributed impulsive controller is obtained. Two illustrated examples are given to illustrate the proposed approach. [ABSTRACT FROM AUTHOR]

This paper investigates the group synchronization of coupled harmonic oscillators over a directed network topology in the absence of velocity measurements. Each harmonic oscillator can only obtain the sampled position states relative to its neighbors at a series of discrete-time instants. Two distributed control protocols are proposed based on the impulsive control and sampled-data control strategies. Theoretical analysis shows that the desired sampling period is determined by the position gain and the eigenvalues of the Laplacian matrix associated with the network topology. Some necessary and sufficient conditions for group synchronization are analytically established in virtue of matrix analysis, graph theory and polynomial Schur stability theory. Different to the synchronization criteria presented in the form of linear matrix inequality or general inequality, which may need to be verified, this paper explicitly gives the ranges for all feasible sampling periods. A significant feature of the synchronization criteria is that certain functional relationships between the feasible sampling period, the largest real part of the eigenvalues of the Laplacian matrix, the largest ratio of the imaginary part to the real part of the eigenvalues of the Laplacian matrix (if there exist complex eigenvalues) and the position gain are analytically established. Some effective iterative methods are then derived to calculate the endpoints of the feasible range of the sampling periods for achieving group synchronization. Finally, numerical experiments further verify the correctness of the theoretical results. [ABSTRACT FROM AUTHOR]

In the framework of sampled-data control, this paper deals with the lag synchronization of chaotic neural networks with time delay meanwhile taking the impulsive control into account. By constructing a proper Lyapunov function and employing the impulsive control theory, some sufficient conditions for lag synchronization of the addressed chaotic neural networks are derived in terms of linear matrix inequalities (LMIs). The hybrid controller including sampled-data controller and impulsive controller is designed based on the established LMIs. A numerical example is provided to demonstrate the effectiveness and advantage of the obtained results. [ABSTRACT FROM AUTHOR]

This paper focuses on the exponential synchronization of nonlinearly coupled Markovian jumping complex dynamical networks with stochastic perturbations under delayed impulsive controller. The Markovian jumping parameters are represented as a continuous-time, finite-state Markov chain. The impulsive control law is defined with both distributed as well as discrete time-varying delays. By designing the efficient impulsive control strategy and by using the Lyapunov method and Ito's formula, some simple and easily realized adequate conditions that assure the exponential synchronization of considered complex dynamical networks are derived in mean square sense. Finally, some simulation results are granted to display the effects of the theoretical findings. [ABSTRACT FROM AUTHOR]

In this paper, an intermittent control approach with multiple switched periods is proposed for the finite-time synchronization in complex networks with non-delay and time-varying delay couplings. Based on finite-time stability theory, the theory of Kronecker product of matrices and the inequality techniques, some novel delay-dependent criteria are obtained to ensure finite-time synchronization for the complex networks, which avoid complex computation on the matrix inequalities. Moreover, the convergence time does not depend on control widths and control periods for the proposed intermittent controller with multiple switched periods. When the control width index $$\theta \rightarrow 1^-$$ , the finite-time impulsive synchronization control schemes as special cases are also given. Especially, the traditional synchronization criteria for some models are improved in the convergence time by using the novel periodical intermittent feedback control and the finite-time impulsive control. The results here are also applicable to both directed and undirected weighted networks without any other conditions. Finally, one numerical example with chaotic nodes is given to demonstrate the effectiveness of the proposed controllers. [ABSTRACT FROM AUTHOR]

This paper investigates the issue of exponential synchronization for a class of nonlinearly coupled complex networks with hybrid time-varying delays by applying impulsive control protocol. It should be mentioned we need not to assume the synchronization state since it may be difficult to find an appropriate function or dynamics to describe the synchronization manifold. By employing the Lyapunov method combined with average impulsive interval as well as the comparison principle, a set of simple and easily verifiable sufficient conditions are derived to guarantee the exponential synchronization for any initial values. Meanwhile, the exponential convergence rate can be specified through the analysis of the networks. Additionally, some numerical examples are given to verify the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the multi-tracking of second-order multi-agent systems. A distributed impulsive protocol is designed to solve the multi-tracking problem, which utilizes only position sampled data of the agents and the desired trajectories. In the context of constant desired velocities, a necessary and sufficient condition on feedback gains and sampling period is obtained to guarantee uniform multi-tracking. In the context of time-varying desired velocities, multi-agent systems can reach bounded variable multi-tracking, in which the ultimate tracking error is proportional to the sampling period. Simulation examples are given to illustrate the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, a pinning impulsive control scheme is adopted to investigate the synchronization of fractional complex dynamical networks. An effective method has been applied to select controlled nodes at each impulsive constants. Based on the Lyapunov function method and the connection between the exponential function and Mittag-Leffler function, sufficient conditions for achieving exponential synchronization of fractional complex networks have been derived. Finally, numerical simulations are exploited to verify the effectiveness of the theoretical results, and some discussions about synchronization region are given. [ABSTRACT FROM AUTHOR]

In this paper, mixed outer synchronization between two different complex dynamical networks without and with time-varying delayed couplings is investigated. By pinning only a fraction of the nodes in the response network, some effective mixed outer synchronization criteria are obtained based on the Lyapunov stability theory. As a result, the mixed outer synchronization between two complex networks is achieved. Then, in the view of the generalized time-varying delayed different inequalities, some sufficient conditions for mixed outer exponential synchronization are derived by imposing the impulsive controllers to the nodes of the corresponding response network. Finally, some numerical simulations are presented to demonstrate the effectiveness and feasibility of the results we obtained in this paper. [ABSTRACT FROM AUTHOR]

This work is concerned with anti-synchronization and intermittent anti-synchronization of two identical hyperchaotic Chua systems using an impulsive control technique. Sufficient condition of anti-synchronization is derived from Lyapunov stability theory, and numerical simulation results are presented to demonstrate the effectiveness of the proposed anti-synchronization scheme. In addition, we report an interesting phenomenon: when the second state of the response system is controlled via impulse, there exist narrow regions of the impulsive control gain, where intermittent anti-synchronization can occur. [ABSTRACT FROM AUTHOR]

In this paper, the issue on impulsive control and synchronization of nonlinear system with impulse time window are investigated. The considered impulsive effects can be stochastically occurred at a determined time window. Hence, the impulses here can be more general and more applicable than the fixed impulses. Some novel and easy-to-check criteria with impulse time window are obtained to guarantee the impulsive control and synchronization global asymptotical stable. Especially, on the basis of the our analysis, we only choose an efficient impulse time window instead of choosing fixed-impulse sequences. Finally, the simulation results further demonstrate the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of fuzzy impulsive control to synchronize two chaotic systems using a novel time-dependent Lyapunov function approach. Compared with the existing time-independent Lyapunov methods, the proposed method enables us to exploit more information on the impulsive intervals. Initially, using the Lyapunov technique and two parameterized linear matrix inequality (LMI) techniques, some less conservative synchronization criteria via a fuzzy impulsive controller using the states of both drive and response chaotic systems are derived. Subsequently, an LMI approach to designing such a fuzzy impulsive controller is developed to realize the synchronization. Finally, the proposed method is applied to the chaotic Lorenz system and Rösler system to illustrate its effectiveness. [ABSTRACT FROM AUTHOR]

In this paper we consider a class of impulsive Caputo fractional-order cellular neural networks with time-varying delays. Applying the fractional Lyapunov method and Mittag-Leffler functions, we give sufficient conditions for global Mittag-Leffler stability which implies global asymptotic stability of the network equilibrium. Our results provide a design method of impulsive control law which globally asymptotically stabilizes the impulse free fractional-order neural network time-delay model. The synchronization of fractional chaotic networks via non-impulsive linear controller is also considered. Illustrative examples are given to demonstrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, impulsive synchronization of drive-response complex-variable chaotic systems is investigated. The drive-response systems with known parameters is considered via impulsive control and adaptive scheme as well as systems with unknown parameters. Noticeably, adaptive strategy is adopted to relax the restriction on the impulsive interval, and the system parameters need not to be known beforehand. According to the Lyapunov stability theory, some synchronization criteria are derived and verified by several numerical simulations. [ABSTRACT FROM AUTHOR]

The objective of this paper is to develop a simple active control scheme for the systems presented in a companion paper (Part I). These are the single mass, the baton, and the three-mass (one revolute joint, two links) systems. The three systems can generate a rich set of passive gaits such as hopping, tapping, and walking each including various gait modes. Yet, we have shown that none of these gait patterns are asymptotically stable except the passive walking. Our control objective is to generate asymptotically stable gait patterns by emulating contact based conditions of passive gaits via impulsive control for the three generations of the family. We consider an impulsive actuator located at all the point masses to actively emulate the contact based rules of passive gait patterns that we introduced in Part I. Consequently, a nonlinear impulsive controller is designed for the hybrid dynamics of our systems that can actively generate the passive gaits on arbitrary ground slope angles. Furthermore, the role of continuous control in the closed loop dynamics of the three-mass system is investigated. We show a combination of continuous and impulsive control can maintain a nonscuffing bipedal walking on arbitrary ground slope angles. Our results show that the controlled systems successfully generate active gaits without significant degradation in the energetic efficiencies of the equivalent passive systems. [ABSTRACT FROM AUTHOR]

This paper includes the latest results of our research effort in developing a family of energetically efficient robots that can produce stable gait. Gravity powered bipeds provide ample proof for the possibility of designing robots that can walk using minimal energy. It is conceivable that mechanisms that are much simpler than legged robots can also produce gravity powered locomotion. In this paper, we present the results of our study of the first three generations of the family: a single mass, a two-mass, and a three-mass system. We show that these three systems can generate a rich set of passive gaits such as hopping, tapping, and walking each including various gait modes. These periodic passive gaits are sustained based on conditions for the physical parameters of the systems. We have developed a preliminary ' contact based rule of passive gait patterns' that seems to work well for the first three generations of the family. We think that this rule can be extended to more complex generations of the family. The control issues are presented in Part II of this paper. [ABSTRACT FROM AUTHOR]

In this paper, the dynamical behavior of a linear Hamiltonian system under two kinds of impulsive control is discussed by means of both theoretical and numerical ways. The existence and stability of the periodic solution are investigated. Moreover, the conditions of existence for a Neimark-Sacker bifurcation are derived by using a discrete map. Numerical results for phase portraits, periodic solutions, and bifurcation diagrams are in good agreement with the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the impulsive control and synchronization of a new unified hyperchaotic system. This new system unifies both the hyperchaotic Lorenz system and the hyperchaotic Chen system. Some conditions are given to guarantee the global asymptotic stability of the controlled and synchronized system. The control gains and impulsive intervals are both variable. Moreover, we estimate the upper bound of impulsive interval for stable control and synchronization. Simulations are included to show the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, projective synchronization of drive-response coupled dynamical network with delayed system nodes and coupling time-varying delay is investigated via impulsive control, where the scaling factors are different from each other. Different controllers are designed to achieve the projective synchronization: only impulsive control is used when the scaling factors need extra limitation, while an extra controller, that is, a simple linear feedback controller, is added when the scaling factors don't need extra limitation. Based on the stability analysis of the impulsive functional differential equation, the sufficient conditions for achieving projective synchronization of such coupled network are established, and an estimate of the upper bound of impulsive intervals ensuring global exponential synchronization of drive-response coupled dynamical network is also given. Numerical examples on the time-delay Lorenz chaotic systems are presented finally to illustrate the effectiveness and advantage of the proposed synchronization criteria. [ABSTRACT FROM AUTHOR]

The electro-mechanical gyrostat system has become a fundamental model of nonlinear dynamics due to its potential applications in practical engineering. It has also been intensively investigated in the last few years due to its intrinsic and complex nonlinear dynamical behaviors. This paper is mainly concerned on the issues of impulsive stabilization and synchronization of chaotic electro-mechanical gyrostat systems. Based on the practical stability theory of impulsive dynamical systems, some simple yet less conservative criteria ensuring impulsive stabilization and synchronization of electro-mechanical gyrostat systems are derived. Subsequently, numerical simulations are presented to demonstrate the effectiveness of the proposed control techniques. [ABSTRACT FROM AUTHOR]

Synchronization between the driving network and the responding network (outer synchronization) has attracted increasing attention from various fields of science and engineering. In this paper, we address outer synchronization of complex networks with delays. Both the cases of coupling delay and node delay are considered. Employing the impulsive control method which is simple, efficient, low cost, and easy to implement in practical applications, we obtain some sufficient conditions of outer synchronization. It indicates that outer synchronization can be achieved if the maximal impulsive intervals are less than a critical value. Numerical simulations are also given to demonstrate the effectiveness of the proposed impulsive control scheme. [ABSTRACT FROM AUTHOR]

This paper studies the projective synchronization in a driven-response dynamical network with coupling time-varying delay model via impulsive control, in which the weights of links are time varying. Based on the stability analysis of the impulsive functional differential equations, some sufficient conditions for the projective synchronization are derived. Numerical simulations are provided to verify the correctness and effectiveness of the proposed method and results. [ABSTRACT FROM AUTHOR]

This paper mainly investigates the projective and lag synchronization between general complex networks via impulsive control. A general drive complex network and an impulsively controlled slave network are presented in the model. Specially, the coupling matrix in this model is not assumed to be symmetric, diffusive or irreducible. Some criteria and corollaries are, respectively, derived for the projective synchronization and lag synchronization between the presented impulsively controlled complex networks. Finally, the results are illustrated by complex networks composed of the chaotic Lorenz systems. All the numerical simulations verify the correctness of the theoretical results. [ABSTRACT FROM AUTHOR]