Time-delay Interval Research Articles

Asynchronous output feedback dissipative control of Markovian jump systems with input time delay and quantized measurements

This paper considers dynamic output-feedback control for Markovian jump systems with input mode-dependent interval time delay and quantized measurements. The transitions of the considered system and the desired output feedback controllers are considered to be asynchronous. The transition probabilities of output feedback controllers are allowed to be known, uncertain, and unknown. The main purpose of this paper is to design an asynchronous output feedback controller for Markov jump systems so that the closed-loop system is stochastically stable and achieves strict (Q,S,R)−α dissipativity. A sufficient condition is developed using Lyapunov functional approach. The controller gains are derived by solving a set of linear matrix inequalities. A numerical example is provided to demonstrate the effectiveness of the developed techniques.

Pinning Synchronization of Multiplex Delayed Networks With Stochastic Perturbations.

As the monoplex network has its limitations in describing the real world, a new framework called the multiplex network is put forward and has received much attention in recent years. This paper focuses on synchronization of the multiplex network with multiple delays and stochastic perturbations. Due to the complexity, pinning control of the multiplex network is of particular interest. Based on the LaSalle-type invariance principle for stochastic differential delay equations and the Lyapunov stability theory, some control schemes and synchronization criteria are obtained. It is concluded that under some mild conditions, one can determine which nodes should be pinned in a multiplex network. In addition, it is found that the number of pinned nodes increases with the varying interval of noise and time delay, and decreases with the varying interval of intralayer coupling strength. Some two-layer and three-layer networks are employed to validate the effectiveness of the proposed algorithm.

Real‐Time Imaging of Ultrafast Charge Dynamics in Tetrafluoromethane from Attosecond Pump‐Probe Photoelectron Spectroscopy

A pump-probe experiment in the tetrafluoro-methane (CF4 ) molecule has been theoretically simulated, allowing one to access electron dynamics in its natural time scale: the attosecond. The chosen pump and probe pulses can be currently produced in most attosecond laboratories. In this scheme, CF4 is first ionized by an extreme UV (XUV) attosecond pulse and the charge dynamics induced in the corresponding cation is probed with a few-femtosecond visible light (VIS) pulse. We demonstrate that modulations in the calculated photoelectron spectra with the pump-probe delay reflect the dynamics of the XUV-induced electronic wave packet. In particular, from the analysis of these modulations in the interval of time delays where the pump and probe pulses do not overlap any more, one has access to the amplitudes and phases of the different components of the electronic wave packet generated by the attosecond pulse. These reflect a complex dynamics that basically consists of very fast charge fluctuations occurring all over the molecule without any preference for a particular molecular site.

Finite-Time Control for Switched Linear Systems with Interval Time-Delay

In this study, finite-time control of switched linear systems with interval time-delay is considered. State feedback is applied in order to ensure finite-time boundedness of the system. Sufficient conditions and average dwell-time bounds are obtained. Because of non-convex terms in the average dwell-time constraint, a technique which converts the nonlinear terms into linear matrix inequality conditions is expressed in terms of the cone-complementarity linearization method. Finally, numerical examples are given for the effectiveness and validity of the proposed solutions.

Exploring tunneling time by instantaneous ionization rate in strong-field ionization.

A quantum approach is presented to investigate tunneling time by supervising the instantaneous ionization rate. We find that the ionization rate peak appearance lags behind the maximum of electric field intensity for a linearly polarized pulse. This time delay interval can be taken to characterize the tunneling time. In addition, if an atom with anisotropic electronic distribution is exposed to a circular polarized pulse, the tunneling time can also be measured and defined as the time difference between the instant of the largest ionization rate and the moment when the electric field points in the maximum of the bound electron density.

Consensus on intervals of communication delay

This paper brings out a structured methodology for identifying intervals of communication time-delay where consensus in directed networks of multiple agents with high-order integrator dynamics is achieved. It is built upon the stability analysis of a transformed consensus problem which preserves all the nonzero eigenvalues of the Laplacian matrix of the associated communication topology graph. It is shown that networks of agents with first-order integrator dynamics can be brought to consensus independently of communication delay, on the other hand, for agents with second-order integrator dynamics, the consensus is achieved independently of communication delay only if certain conditions are satisfied. Conversely, if such conditions are not satisfied, it is shown how to compute the intervals of communication delay where multiple agents with second-order or higher-order can be brought to consensus. The paper is ended by showing an interesting example of a network of agents with second-order integrator dynamics which is consensable on the first time-delay interval, but as the time-delay increases, it loses consensability on the second time-delay interval, then it becomes consensable again on the third time-delay interval, and finally it does not achieve consensus any more on the fourth time-delay interval. This example shows the importance of analyzing consensus with time-delay in different intervals.

Positive observer design for linear impulsive positive systems with interval uncertainties and time delay

This paper is concerned with the problem of positive observer design for impulsive positive systems (IPS) with interval uncertainties and time delay. A copositive Lyapunov-Krasovskii functional with exponential term is constructed. By applying the average impulsive interval method, sufficient conditions for the existence of the positive observer are established to guarantee the exponential stability of the corresponding augmented system, which ensures the designed positive observer can estimate the system states exponentially. Combined with the linear programming (LP) technique, an algorithm is developed to design the observer gain matrices. Finally, a numerical example is provided to show the effectiveness of the theoretical results.

Stability of neutral type fractional delay systems and its relation with stability of time‐delay and discrete systems

The bounded-input bounded-output stability of fractional delay systems of neutral type is investigated in this study. The proposed method calculates the number of unstable poles of the system for each delay value. All time-delay intervals in time-delay space where system is stable are precisely determined. The stability of systems with not only indefinitely large values of time-delay, but also with multiple poles on the imaginary axis has been studied. The proposed method is employed for investigating the stability of a fractional delay system when its fractional orders approach to the integer numbers or zero. It is proved that simple case of neutral types and time-delay systems have the same conditions for the independent stability. Two numerical examples are provided to illustrate the proficiencies of the proposed method.

Research on Time Delay Stability of Power System using Fault Chains and Markov Process

A new method based on fault chains and the Markov process for analyzing time-delay power system stability is proposed in this article. First, reasonable fault chains are formed using the fault chain generation method based on network power flow. Second, by combining the fault chains and Markov processes, a class of Lyapunov–Krasovskii functionals considering the Markov jump is established. Free weighting items constructed with the Markov process transfer rate matrix and Newton–Leibniz formula, respectively, are then introduced to the weak infinitesimal operators in the Lyapunov–Krasovskii functional. Meanwhile, to lower the conservativeness of the method, the whole time-varying time-delay interval has been divided into two subintervals. Finally, the time-delay upper bound that the power system can bear in the case of cascading faults is calculated by means of the generalized eigenvalue problem. The efficiency and feasibility of the proposed method in solving the maximum time delay in the case of cascading faults have been validated by the dynamic time-domain simulation results. Comparative results with other methods show the proposed method has low conservativeness.

Determination of the Basic Parameters of the Recovery Process for Extracting Iron from Iron and Steel Slag

The paper identifies the effect of temperature recovery on the iron slag output in the steel industry, the value of which is recommended to take in the range of 1600 – 1650 °C. Laboratory studies were carried out in an oven Tamman resistance. Studies have shown that an increase in the time delay interval in the molten slag 1300 – 1650 °C higher than the degree of metal removal. With the use of statistical processing dependences for determination of content of FeO content in the converter and open-hearth slag were received.

Some novel approaches on state estimation of delayed neural networks

This paper studies the issue of state estimation for a class of neural networks (NNs) with time-varying delay. A novel Lyapunov-Krasovskii functional (LKF) is constructed, where triple integral terms are used and a secondary delay-partition approach (SDPA) is employed. Compared with the existing delay-partition approaches, the proposed approach can exploit more information on the time-delay intervals. By taking full advantage of a modified Wirtinger’s integral inequality (MWII), improved delay-dependent stability criteria are derived, which guarantee the existence of desired state estimator for delayed neural networks (DNNs). A better estimator gain matrix is obtained in terms of the solution of linear matrix inequalities (LMIs). In addition, a new activation function dividing method is developed by bringing in some adjustable parameters. Three numerical examples with simulations are presented to demonstrate the effectiveness and merits of the proposed methods.

Impulsive control for the synchronization of coupled neural networks with reaction–diffusion terms

The impulsive control method is utilized to achieve the synchronization of coupled reaction–diffusion neural networks with time-varying delay. By combining the Lyapunov functional method with the impulsive delay differential inequality and comparison principle, a few sufficient conditions are derived to guarantee the global exponential synchronization of coupled neural networks with reaction–diffusion terms. Especially, the estimate for the exponential convergence rate is also given, which relies on time delay, system parameters and impulsive interval. Finally, numerical examples are provided to demonstrate the correctness and effectiveness of our results.

Optimal Time to Surgery for Patients Requiring Laparoscopic Appendectomy: An Integrative Review

Acute appendicitis is the most common condition requiring emergency surgery worldwide. Although current guidelines recommend prompt appendectomy as the preferred treatment, no time interval for surgery has been indicated. We used an integrative review methodology to critically evaluate evidence on the relationship between time to surgery and hospital length of stay and to identify the ideal time to surgery for patients undergoing appendectomy. We included 14 studies in our synthesis, most of which (n = 9/14, 64%) indicated that longer time delays to surgical intervention increased hospital length of stay for patients presenting with appendicitis. Researchers report that the optimal time for surgery is 24 to 36 hours after symptom onset, or 10 to 24 hours from admission. The results of our review indicate that patient symptoms on presentation may signify advancing pathology and may be more important than the time delay interval in defining surgical priority.

Robust dynamic output feedback fault-tolerant control for Takagi-Sugeno fuzzy systems with interval time-varying delay via improved delay partitioning approach

Abstract This paper addresses the problem of robust fault-tolerant control design scheme for a class of Takagi-Sugeno fuzzy systems subject to interval time-varying delay and external disturbances. First, by using improved delay partitioning approach, a novel n-steps iterative learning fault estimation observer under H ∞ constraint is constructed to achieve estimation of actuator fault. Then, based on the online estimation information, a fuzzy dynamic output feedback fault-tolerant controller considered interval time delay is designed to compensate for the impact of actuator faults, while guaranteing that the closed-loop system is asymptotically stable with the prescribed H ∞ performance. Moreover, all the obtained less conservative sufficient conditions for the existence of fault estimation observer and fault-tolerant controller are formulated in terms of linear matrix inequalities. Finally, the numerical examples and simulation results are presented to show the effectiveness and merits of the proposed methods.

Dynamics of Time Delay-Induced Multiple Synchronous Behaviors in Inhibitory Coupled Neurons

The inhibitory synapse can induce synchronous behaviors different from the anti-phase synchronous behaviors, which have been reported in recent studies. In the present paper, synchronous behaviors are investigated in the motif model composed of reciprocal inhibitory coupled neurons with endogenous bursting and time delay. When coupling strength is weak, synchronous behavior appears at a single interval of time delay within a bursting period. When coupling strength is strong, multiple synchronous behaviors appear at different intervals of time delay within a bursting period. The different bursting patterns of synchronous behaviors, and time delays and coupling strengths that can induce the synchronous bursting patterns can be well interpreted by the dynamics of the endogenous bursting pattern of isolated neuron, which is acquired by the fast-slow dissection method, combined with the inhibitory coupling current. For an isolated neuron, when a negative impulsive current with suitable strength is applied at different phases of the bursting, multiple different bursting patterns can be induced. For a neuron in the motif, the inhibitory coupling current, of which the application time and strength is modulated by time delay and coupling strength, can cause single or multiple synchronous firing patterns like the negative impulsive current when time delay and coupling strength is suitable. The difference compared to the previously reported multiple synchronous behaviors that appear at time delays wider than a period of the endogenous firing is discussed. The results present novel examples of synchronous behaviors in the neuronal network with inhibitory synapses and provide a reasonable explanation.

Delay-range-dependent control of nonlinear time-delay systems under input saturation

Summary This paper describes a delay-range-dependent local state feedback controller synthesis approach providing estimation of the region of stability for nonlinear time-delay systems under input saturation. By employing a Lyapunov–Krasovskii functional, properties of nonlinear functions, local sector condition and Jensen's inequality, a sufficient condition is derived for stabilization of nonlinear systems with interval delays varying within a range. Novel solutions to the delay-range-dependent and delay-dependent stabilization problems for linear and nonlinear time-delay systems, respectively, subject to input saturation are derived as specific scenarios of the proposed control strategy. Also, a delay-rate-independent condition for control of nonlinear systems in the presence of input saturation with unknown delay-derivative bound information is established. And further, a robust state feedback controller synthesis scheme ensuring L2 gain reduction from disturbance to output is devised to address the problem of the stabilization of input-constrained nonlinear time-delay systems with varying interval lags. The proposed design conditions can be solved using linear matrix inequality tools in connection with conventional cone complementary linearization algorithms. Simulation results for an unstable nonlinear time-delay network and a large-scale chemical reactor under input saturation and varying interval time-delays are analyzed to demonstrate the effectiveness of the proposed methodology. Copyright © 2015 John Wiley & Sons, Ltd.

Static State-Feedback Controller and Observer Design for Interval Positive Systems With Time Delay

This brief is concerned with the design of observer-based controllers for continuous-time positive linear systems with interval uncertainties and time delay. More precisely, the problem of positive stabilization by observer-based static state-feedback controllers is investigated, taking into account that the nonnegativity of the error signals and the positivity of the augmented system are necessary to guarantee the stability of the closed-loop system and keep it positive at the same time. The proposed design methodology, which is based on linear matrix inequality conditions, is also illustrated by an example.

Guaranteed interval of delay for a class of non-linear control systems

A new method is proposed in this article in order to determine a guaranteed interval of time delay in input signal for a class of non-linear control systems with state feedback. This method is based on the stability sufficient condition of a non-linear control system using the Lyapunov direct approach. For this purpose, the dynamic equations of the non-linear input-delayed system are reformulated as a non-linear system without delay, but with delay-dependent coefficients in the state-space description. The control strategy is considered a linear state feedback. Then, by introducing an appropriately related Lyapunov candidate, the stability sufficient condition of the closed-loop system is satisfied, leading to a guaranteed interval of delay according to the state feedback gain. The main results are gathered and proved as a lemma. The effectiveness of this proposed method is investigated by simulating the state feedback control of a non-linear synchronous generator with a delay in input.

Adaptive mechanism for synchronization of chaotic oscillators with interval time-delays

This paper addresses the adaptive feedback controller design for the synchronization of chaotic systems with interval time-delays in their state vectors by exploiting a lower and an upper bound on time-delays. Simple control and adaptation laws are developed for chaos synchronization, and linear matrix inequalities (LMIs) are derived to ensure asymptotic convergence of the synchronization error between the master–slave systems, using the proposed feedback control strategy, by employing a novel treatment of Lyapunov–Krasovskii functional. Further, the proposed strategy is strengthened by exploiting \(L_2 \) stability against disturbances and perturbations and corresponding LMIs for robust adaptive controller synthesis are derived. Furthermore, a novel delay-range-dependent robust adaptive synchronization control approach for dealing with locally Lipschitz non-delayed and delayed nonlinearities in the dynamics of chaotic oscillators is provided by employing an additional adaptation law for the nonlinearities. A numerical simulation example is provided to illustrate effectiveness of the proposed synchronization approach.

Consensus on Time-Delay Intervals in Networks of High-Order Integrator Agents

This paper brings out a structured methodology for identifying time-delay intervals where consensus in directed networks of multiple agents with high-order integrator dynamics is achieved. It is built upon the stability analysis of a transformed consensus problem. Furthermore, particular results are derived for networks of agents with first-and second-order integrator dynamics, which can be consensusable only on the first time-delay interval, showing the value of the upper bound of this interval. The paper is closed by showing an interesting example of a network of third-order integrator agents that is not consensusable when free of delay, but it is consensusable when the control input is delayed in a proper interval.