Pinning Synchronization of Discrete-Time Complex Networks with Different Time-Varying Delays

This paper investigates pinning synchronization of discrete-time complex networks with differen t time-varying delays.An important lemma is presen ted and proved,t hen detailed analysis is given to yield some synchronization criteria for this kind of net works.The results provide an effective way to synchronize discrete-time complex networks by reducing control cost.Furthermore,these theoretical results are illustrated by a complex network via two kinds of pinning schemes.Numerical simulations verify the feasibil计y of the proposed methods.

New results on global exponential stability of competitive neural networks with different time scales and time-varying delays

This paper studies the global exponential stability of competitive neural networks with different time scales and time-varying delays. By using the method of the proper Lyapunov functions and inequality technique, some sufficient conditions are presented for global exponential stability of delay competitive neural networks with different time scales. These conditions obtained have important leading significance in the designs and applications of global exponential stability for competitive neural networks. Finally, an example with its simulation is provided to demonstrate the usefulness of the proposed criteria.

Position Measurement Based Slave Torque Feedback Control for Teleoperation Systems With Time-Varying Communication Delays

Bilateral teleoperation system is referred to as a promising technology to extend human actions and intelligence to manipulating objects remotely.For the tracking control of teleoperation systems,velocity measurements are necessary to provide feedback information.However,due to hardware technology and cost constraints,the velocity measurements are not always available.In addition,the time-varying communication delay makes it challenging to achieve tracking task.This paper provides a solution to the issue of real-time tracking for teleoperation systems,subjected to unavailable velocity signals and time-varying communication delays.In order to estimate the velocity information,immersion and invariance(I&I)technique is employed to develop an exponential stability velocity observer.For the proposed velocity observer,a linear relationship between position and observation state is constructed,through which the need of solving partial differential and certain integral equations can be avoided.Meanwhile,the mean value theorem is exploited to separate the observation error terms,and hence,all functions in our observer can be analytically expressed.With the estimated velocity information,a slave-torque feedback control law is presented.A novel Lyapunov-Krasovskii functional is constructed to establish asymptotic tracking conditions.In particular,the relationship between the controller design parameters and the allowable maximum delay values is provided.Finally,simulation and experimental results reveal that the proposed velocity observer and controller can guarantee that the observation errors and tracking error converge to zero.

Interdecadal Variations of Phase Delays Between Two Nino Indices at Different Time Scales

Phase delays between two Nino indices-sea surface temperatures in Nino regions 1+2 and 3.4 (1950-2001)-at different time scales are detected by wavelet analysis. Analysis results show that there are two types of period bifurcations in the Nino indices and that period bifurcation points exist only in the region where the wavelet power is small. Interdecadal variation features of phase delays between the two indices vary with different time scales. In the periods of 40-72 months, the phase delay changes its sign in 1977: Nino 1+2 indices are 2-4 months earlier than Nino 3.4 indices before 1977, but 3-6 months later afterwards. In the periods of 20-40 months, however, the phase delay changes its sign in another way: Nino 1+2 indices are 1-4 months earlier before 1980 and during 1986-90, but 1-4 months later during 1980-83 and 1993-2001.

Sufficient conditions of the various stabilities of the linear time-varying delayed differential equations

Due to the appearance and the study of the ornithopter and flexible-wing micro air vehicles, etc., the time-varying systems become more and more important and ubiquitous in the study of the mechanics. In this letter, the sufficient conditions of the uniform asymptotic stability are first presented for the delayed time-varying linear differential equations with any time delay by employing the Dini derivative, Lozinskii measure and the generalized scalar Halanay delayed differential inequality. They are especially based on the estimation of the arbitrary solutions but not the fundamental solution matrix since their solutions＇ space is infinite-dimensional. Then some sufficient conditions of the stability, asymptotic stability and uniform asymptotic stability of the delayed time-varying linear system with a sufficiently small time delay are reported by employing Taylor expansion and Dini derivative. It implies that these stabilities can be guaranteed by the Lozinskii measure of the matrix composing of the time delay and the coefficient matrices of the system.

Fixed-Time Adaptive Time-Varying Matrix Projective Synchronization of Time-Delayed Chaotic Systems with Different Dimensions

This paper deals with the fixed-time adaptive time-varying matrix projective synchronization(ATVMPS)of different dimensional chaotic systems(DDCSs)with time delays and unknown parameters.Firstly,to estimate the unknown parameters,adaptive parameter updated laws are designed.Secondly,to realize the fixed-time ATVMPS of the time-delayed DDCSs,an adaptive delay-unrelated controller is designed,where time delays of chaotic systems are known or unknown.Thirdly,some simple fixed-time ATVMPS criteria are deduced,and the rigorous proof is provided by employing the inequality technique and Lyapunov theory.Furthermore,the settling time of fixed-time synchronization(Fix-TS)is obtained,which depends only on controller parameters and system parameters and is independent of the system’s initial states.Finally,simulation examples are presented to validate the theoretical analysis.

Consensus of high-order dynamic multi-agent systems with switching topology and time-varying delays

This paper studies the consensus problems for a group of agents with switching topology and time-varying communication delays, where the dynamics of agents is modeled as a high-order integrator. A linear distributed consensus protocol is proposed, which only depends on the agent＇s own information and its neighbors＇ partial information. By introducing a decomposition of the state vector and performing a state space transformation, the closed-loop dynamics of the multi-agent system is converted into two decoupled subsystems. Based on the decoupled subsystems, some sufficient conditions for the convergence to consensus are established, which provide the upper bounds on the admissible communication delays. Also, the explicit expression of the consensus state is derived. Moreover, the results on the consensus seeking of the group of high-order agents have been extended to a network of agents with dynamics modeled as a completely controllable linear time-invariant system. It is proved that the convergence to consensus of this network is equivalent to that of the group of high-order agents. Finally, some numerical examples are given to demonstrate the effectiveness of the main results.

Guaranteed Cost Consensus for High-dimensional Multi-agent Systems With Time-varying Delays

Guaranteed cost consensus analysis and design problems for high-dimensional multi-agent systems with time varying delays are investigated. The idea of guaranteed cost con trol is introduced into consensus problems for high-dimensiona multi-agent systems with time-varying delays, where a cos function is defined based on state errors among neighboring agents and control inputs of all the agents. By the state space decomposition approach and the linear matrix inequality(LMI)sufficient conditions for guaranteed cost consensus and consensu alization are given. Moreover, a guaranteed cost upper bound o the cost function is determined. It should be mentioned that these LMI criteria are dependent on the change rate of time delays and the maximum time delay, the guaranteed cost upper bound is only dependent on the maximum time delay but independen of the Laplacian matrix. Finally, numerical simulations are given to demonstrate theoretical results.

Event-triggered Tracking Consensus with Packet Losses and Time-varying Delays

This paper mainly investigates the event-triggered tracking control for leader-follower multi-agent systems with the problems of packet losses and time-varying delays when both the first-order and the second-order neighbors' information are used. Event-triggered control laws are adopted to reduce the frequency of individual actuation updating under the sampleddata framework for discrete-time agent dynamics. The communication graph is undirected and the loss of data across each communication link occurs at certain probability, which is governed by a Bernoulli process. One numerical example is given to demonstrate the effectiveness of the proposed methods.It is found that the tracking consensus is sped up by using the second-order neighbors' information when packet losses and time-varying delays occur.

Observer-based Adaptive Iterative Learning Control for Nonlinear Systems with Time-varying Delays

An observer-based adaptive iterative learning control （AILC） scheme is developed for a class of nonlinear systems with unknown time-varying parameters and unknown time-varying delays. The linear matrix inequality （LMI） method is employed to design the nonlinear observer. The designed controller contains a proportional-integral-derivative （PID） feedback term in time domain. The learning law of unknown constant parameter is differential-difference-type, and the learning law of unknown time-varying parameter is difference-type. It is assumed that the unknown delay-dependent uncertainty is nonlinearly parameterized. By constructing a Lyapunov-Krasovskii-like composite energy function （CEF）, we prove the boundedness of all closed-loop signals and the convergence of tracking error. A simulation example is provided to illustrate the effectiveness of the control algorithm proposed in this paper.

Adaptive Variable Structure Control of MIMO Nonlinear Systems with Time-varying Delays and Unknown Dead-zones

In this paper, adaptive variable structure neural control is presented for a class of uncertain multi-input multi-output （MIMO） nonlinear systems with state time-varying delays and unknown nonlinear dead-zones. The unknown time-varying delay uncer- tainties are compensated for using appropriate Lyapunov-Krasovskii functionals in the design. The approach removes the assumption of linear function outside the deadband without necessarily constructing a dead-zone inverse as an added contribution. By utilizing the integral-type Lyapunov function and introducing an adaptive compensation term for the upper bound of the residual and optimal approximation error as well as the dead-zone disturbance, the closed-loop control system is proved to be semi-globally uniformly ultimately bounded. In addition, a modified adaptive control algorithm is given in order to avoid the high-frequency chattering phenomenon. Simulation results demonstrate the effectiveness of the approach.

Multi-agent consensus with time-varying delays and switching topologies

The consensus problems of multi-agents with time-varying delays and switching topologies are studied. First, assume that an agent receives state information from its neighbors with fixed communication delays and processes its own state information with time-varying self-delay respectively. The state time-delay feedback is introduced into the existing consensus protocol to begenerate an improved protocol. Then a sufficient condition is derived which can make the system with time-varying self-delays achieve the consensus. On this basis, a specific form of consensus equilibrium influenced by the initial states of agents, time-delays and state feedback intensity is figured out. In addition, the multi-agent consensus is considered with time-varying topologies. Finally, simulations are presented to il ustrate the validity of theoretical results.

A new result on global exponential robust stability of neural networks with time-varying delays

In this paper, the global exponential robust stability of neural networks with ume-varying delays is investigated. By using nonnegative matrix theory and the Halanay inequality, a new sufficient condition for global exponential robust stability is presented. It is shown that the obtained result is different from or improves some existing ones reported in the literatures. Finally, some numerical examples and a simulation are given to show the effectiveness of the obtained result.

Improved Exponential Stability Criteria for Recurrent Neural Networks with Time-varying Discrete and Distributed Delays

In this paper, the problem of the global exponential stability analysis is investigated for a class of recurrent neural networks （RNNs） with time-varying discrete and distributed delays. Due to a novel technique when estimating the upper bound of the derivative of Lyapunov functional, we establish new exponential stability criteria in terms of LMIs. It is shown that the obtained criteria can provide less conservative results than some existing ones. Numerical examples are given to show the effectiveness of the proposed results.

Impulsive control of nonlinear systems with time-varying delays

A whole impulsive control scheme of nonlinear systems with time-varying delays, which is an extension for impulsive control of nonlinear systems without time delay, is presented in this paper. Utilizing the Lyapunov functions and the impulsive-type comparison principles, we establish a series of different conditions under which impulsively controlled nonlinear systems with time-varying delays are asymptotically stable. Then we estimate upper bounds of impulse interval and time-varying delays for asymptotically stable control. Finally a numerical example is given to illustrate the effectiveness of the method.

DYNAMICS OF NEW CLASS OF HOPFIELD NEURAL NETWORKS WITH TIME-VARYING AND DISTRIBUTED DELAYS

In this paper, we investigate the dynamics and the global exponential stability of a new class of Hopfield neural network with time-varying and distributed delays. In fact, the properties of norms and the contraction principle are adjusted to ensure the existence as well as the uniqueness of the pseudo almost periodic solution, which is also its derivative pseudo almost periodic. This results are without resorting to the theory of exponential dichotomy. Furthermore, by employing the suitable Lyapunov function, some delayindependent sufficient conditions are derived for exponential convergence. The main originality lies in the fact that spaces considered in this paper generalize the notion of periodicity and almost periodicity. Lastly, two examples are given to demonstrate the validity of the proposed theoretical results.

New results on stability criteria for neural networks with time-varying delays

In this paper, the problem of stability analysis for neural networks with time-varying delays is considered. By constructing a new augmented Lyapunov-Krasovskii＇s functional and some novel analysis techniques, improved delaydependent criteria for checking the stability of the neural networks are established. The proposed criteria are presented in terms of linear matrix inequalities （LMIs） which can be easily solved and checked by various convex optimization algorithms. Two numerical examples are included to show the superiority of our results.

H-infinity control for networked control systems (NCS) with time-varying delays

This paper discusses H-infinity state feedback control for a networked control system with time-varying delays. Based on the flee-weighing matrix method, a dehy-dependent stability criterion satisfying a prescribed H-infinity norm bound is presented for an NCS with unknown, time-varying and bounded delays. And then, the criterion is transformed into sufficient conditions based on linear matrix inequalities for H-infinity control. The conditions thus obtained are also used to design an H-infinity state feedback controller. This design method is further extended to solve the design problem of robust H-infinity state feedback control. A numerical example demonstrates the validity of the method.

Passivity analysis for uncertain stochastic neural networks with discrete interval and distributed time-varying delays

The problem of passivity analysis is investigated for uncertain stochastic neural networks with discrete interval and distributed time-varying delays.The parameter uncertainties are assumed to be norm bounded and the delay is assumed to be time-varying and belongs to a given interval,which means that the lower and upper bounds of interval time-varying delays are available.By constructing proper Lyapunov-Krasovskii functional and employing a combination of the free-weighting matrix method and stochastic analysis technique,new delay-dependent passivity conditions are derived in terms of linear matrix inequalities（LMIs）.Finally,numerical examples are given to show the less conservatism of the proposed conditions.

Robust Output Feedback Control for Fractional Order Nonlinear Systems with Time-varying Delays

Robust controller design problem is investigated for a class of fractional order nonlinear systems with time varying delays.Firstly,a reduced-order observer is designed.Then,an output feedback controller is designed.Both the designed observer and controller are independent of time delays.By choosing appropriate Lyapunov functions,we prove the designed controller can render the fractional order system asymptotically stable.A simulation example is given to verify the effectiveness of the proposed approach.