Editorial: Dynamics on delayed systems

In the representation of natural and social phenom- ena, there exist not only ordinary or partial differential equations which are independent of the past states and determined solely by the present states~ but also time delay differential equations which are related to some of the past states. Time delay is ubiquitous in mechanical, physical, ecological, physiological, biological, economic, electronic, and chemical systems due to finite propaga- tion speeds of signals, finite reaction times, and finite processing times. These realistic backgrounds drive var- ious investigations to consider effects of time delays on realistic phenomena which are modeled by delay differ- ential equations. It is impossible to make achievements only by extending theory of ordinary or partial differen- tial equations since time delay is of uncertainty in time scale. Therefore, the study will be very difficult for a problem in the infinite-dimensional space.

Is the High-Frequency Signal Necessary for the Resonance in the Delayed System?

In a delayed system excited by low-frequency and high-frequency signals, the necessity of the high-frequency signal on the resonance is discussed. By adjusting the delay time, the resonance occurs in a wide scope of frequencies, including the primary, subharmonic and superharmonic frequencies. Only for very few cases does the high-frequency signal have a positive effect on the resonance. It is the traditional vibrational resonance phenomenon. In most situations, the high-frequency excitation is unnecessary for the resonance. An appropriate delay, rather than the high-frequency signal, is the key factor in improving the weak low-frequency signal.

Further Results on Delay-distribution-dependent Robust Stability Criteria for Delayed Systems

This paper concerns the robust stability analysis of uncertain systems with time delays as random variables drawn from some probability distribution. The delay-distribution-dependent criteria for the exponential stability of the original system in mean square sense are achieved by Lyapunov functional method and the linear matrix inequality （LMI） technique. The proposed approach involves neither free weighting matrices nor any model transformation, and it shows that the new criteria can provide less conservative results than some existing ones. Numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method.

Input-to-State Stabilization of Nonlinear Impulsive Delayed Systems: An Observer-Based Control Approach

This paper addresses the problems of input-to-state stabilization and integral input-to-state stabilization for a class of nonlinear impulsive delayed systems subject to exogenous dis-turbances.Since the information of plant’s states,time delays,and exogenous disturbances is often hard to be obtained,the key design challenge,which we resolve,is the construction of a state observer-based controller.For this purpose,we firstly propose a corresponding observer which is independent of time delays and exogenous disturbances to reconstruct(or estimate)the plant’s states.And then based on the observations,we establish an observer-based control design for the plant to achieve the input-to-state stability(ISS)and integral-ISS(iISS)properties.With the help of the comparison principle and average impulse interval approach,some sufficient conditions are presented,and moreover,two different linear matrix inequalities(LMIs)based criteria are proposed to design the gain matrices.Finally,two numerical examples and their simulations are given to show the effectiveness of our theoretical results.

Adaptive control of bifurcation and chaos in a time-delayed system

In this paper,the stabilization of a continuous time-delayed system is considered.To control the bifurcation and chaos in a time-delayed system,a parameter perturbation control and a hybrid control are proposed.Then,to ensure the asymptotic stability of the system in the presence of unexpected system parameter changes,the adaptive control idea is introduced,i.e.,the perturbation control parameter and the hybrid control parameter are automatically tuned according to the adaptation laws,respectively.The adaptation algorithms are constructed based on the Lyapunov-Krasovskii stability theorem.The adaptive parameter perturbation control and the adaptive hybrid control methods improve the corresponding constant control methods.They have the advantages of increased stability,adaptability to the changes of the system parameters,control cost saving,and simplicity.Numerical simulations for a well-known chaotic time-delayed system are performed to demonstrate the feasibility and superiority of the proposed control methods.A comparison of the two adaptive control methods is also made in an experimental study.

Enhancing Design of Visual-Servo Delayed System

A robust adaptive predictor is proposed to solve the time-varying and delay control problem of an overhead crane system with a stereo-vision servo. The predictor is based on the use of a recurrent neural network(RNN) with tapped delays, and is used to supply the real-time signal of the swing angle. There are two types of discrete-time controllers under investigation, i.e., the proportional-integral-derivative(PID) controller and the sliding controller. Firstly, a design principle of the neural predictor is developed to guarantee the convergence of its swing angle estimation. Then, an improved version of the particle swarm optimization algorithm, the parallel particle swarm optimization(PPSO) method is used to optimize the control parameters of these two types of controllers. Finally, a homemade overhead crane system equipped with the Kinect sensor for the visual servo is used to verify the proposed scheme. Experimental results demonstrate the effectiveness of the approach, which also show the parameter convergence in the predictor.

RECURSIVE PARAMETER ESTIMATION OF LINEAR DELAYED SYSTEM VIA NUMERICAL INTEGRAL OPERATION

In this paper,the problem of Parameter estimation in linear delayedsystems from sampled data is treated.Using numerical integral operation(NIO),anidentification model which is parametrized directly in the linear delayed system pa-rameters is got.With the least square(LS)method or the instrumental variable(Ⅳ)method,the recursive algorithm of parameter estimation is given.The result ofthe illustrated example shows that this algorithm is simple,rapid and accurrate.

Robust Stabilization of Delayed Systems with Rank-1 Type Uncertainties

This paper deals with the problem of robust stabilizationfor the systems with rank-1 type uncertainties and mul-tiple state delay.Firstly,a new delay-dependent crite-ria is presented for unforced normal delayed system to bestable.Based on the obtained criteria,a new LMI ap-proach is developed for robust stabilization of a class ofuncertain delay systems via linear memoryless state feed-back control law.The results depend on the size of thedelays and are given in terms of linear matrix inequali-ties.And so no tuning procedure for scalars and/or ma-trices is required and the results are less conservativethan those of delay-independent.Finally,an illustra-tive example is presented.

Designing Proportional-Integral Consensus Protocols for Second-Order Multi-Agent Systems Using Delayed and Memorized State Information

This paper is concerned with consensus of a secondorder linear time-invariant multi-agent system in the situation that there exists a communication delay among the agents in the network.A proportional-integral consensus protocol is designed by using delayed and memorized state information.Under the proportional-integral consensus protocol,the consensus problem of the multi-agent system is transformed into the problem of asymptotic stability of the corresponding linear time-invariant time-delay system.Note that the location of the eigenvalues of the corresponding characteristic function of the linear time-invariant time-delay system not only determines the stability of the system,but also plays a critical role in the dynamic performance of the system.In this paper,based on recent results on the distribution of roots of quasi-polynomials,several necessary conditions for Hurwitz stability for a class of quasi-polynomials are first derived.Then allowable regions of consensus protocol parameters are estimated.Some necessary and sufficient conditions for determining effective protocol parameters are provided.The designed protocol can achieve consensus and improve the dynamic performance of the second-order multi-agent system.Moreover,the effects of delays on consensus of systems of harmonic oscillators/double integrators under proportional-integral consensus protocols are investigated.Furthermore,some results on proportional-integral consensus are derived for a class of high-order linear time-invariant multi-agent systems.

Prescribed Performance Tracking Control of Time-Delay Nonlinear Systems With Output Constraints

The problem of prescribed performance tracking control for unknown time-delay nonlinear systems subject to output constraints is dealt with in this paper. In contrast with related works, only the most fundamental requirements, i.e., boundedness and the local Lipschitz condition, are assumed for the allowable time delays. Moreover, we focus on the case where the reference is unknown beforehand, which renders the standard prescribed performance control designs under output constraints infeasible. To conquer these challenges, a novel robust prescribed performance control approach is put forward in this paper.Herein, a reverse tuning function is skillfully constructed and automatically generates a performance envelop for the tracking error. In addition, a unified performance analysis framework based on proof by contradiction and the barrier function is established to reveal the inherent robustness of the control system against the time delays. It turns out that the system output tracks the reference with a preassigned settling time and good accuracy,without constraint violations. A comparative simulation on a two-stage chemical reactor is carried out to illustrate the above theoretical findings.

Analysis and Design of Time-Delay Impulsive Systems Subject to Actuator Saturation

This paper investigates the exponential stability and performance analysis of nonlinear time-delay impulsive systems subject to actuator saturation. When continuous dynamics is unstable, under some conditions, it is shown that the system can be stabilized by a class of saturated delayed-impulses regardless of the length of input delays. Conversely, when the system is originally stable, it is shown that under some conditions, the system is robust with respect to sufficient small delayed-impulses. Moreover, the design problem of the controller with the goal of obtaining a maximized estimate of the domain of attraction is formulated via a convex optimization problem. Three examples are provided to demonstrate the validity of the main results.

Numerical Analysis of Bacterial Meningitis Stochastic Delayed Epidemic Model through Computational Methods

Based on theWorld Health Organization(WHO),Meningitis is a severe infection of the meninges,the membranes covering the brain and spinal cord.It is a devastating disease and remains a significant public health challenge.This study investigates a bacterial meningitis model through deterministic and stochastic versions.Four-compartment population dynamics explain the concept,particularly the susceptible population,carrier,infected,and recovered.The model predicts the nonnegative equilibrium points and reproduction number,i.e.,the Meningitis-Free Equilibrium(MFE),and Meningitis-Existing Equilibrium(MEE).For the stochastic version of the existing deterministicmodel,the twomethodologies studied are transition probabilities and non-parametric perturbations.Also,positivity,boundedness,extinction,and disease persistence are studiedrigorouslywiththe helpofwell-known theorems.Standard and nonstandard techniques such as EulerMaruyama,stochastic Euler,stochastic Runge Kutta,and stochastic nonstandard finite difference in the sense of delay have been presented for computational analysis of the stochastic model.Unfortunately,standard methods fail to restore the biological properties of the model,so the stochastic nonstandard finite difference approximation is offered as an efficient,low-cost,and independent of time step size.In addition,the convergence,local,and global stability around the equilibria of the nonstandard computational method is studied by assuming the perturbation effect is zero.The simulations and comparison of the methods are presented to support the theoretical results and for the best visualization of results.

Surgical techniques to prevent delayed gastric emptying after pancreaticoduodenectomy

Background: Delayed gastric emptying(DGE) is one of the most common complications after pancreaticoduodenectomy(PD). DGE represents impaired gastric motility without significant mechanical obstruction and is associated with an increased length of hospital stay, increased healthcare costs, and a high readmission rate. We reviewed published studies on various technical modifications to reduce the incidence of DGE. Data sources: Studies were identified by searching Pub Med for relevant articles published up to December 2022. The following search terms were used: “pancreaticoduodenectomy”, “pancreaticojejunostomy”, “pancreaticogastrostomy”, “gastric emptying”, “gastroparesis” and “postoperative complications”. The search was limited to English publications. Additional articles were identified by a manual search of references from key articles. Results: In recent years, various surgical procedures and techniques have been explored to reduce the incidence of DGE. Pyloric resection, Billroth II reconstruction, Braun's enteroenterostomy, and antecolic reconstruction may be associated with a decreased incidence of DGE, but more high-powered studies are needed in the future. Neither laparoscopic nor robotic surgery has demonstrated superiority in preventing DGE, and the use of staplers is controversial regarding whether they can reduce the incidence of DGE. Conclusions: Despite many innovations in surgical techniques, there is no surgical procedure that is superior to others to reduce DGE. Further larger prospective randomized studies are needed.

Delayed neurological dysfunction following posterior laminectomy with lateral mass screw fixation:A case report and review of literature

BACKGROUND While most complications of cervical surgery are reversible,some,such as symptomatic postoperative spinal epidural hematoma(SEH),which generally occurs within 24 h,are associated with increased morbidity and mortality.Delayed neurological dysfunction is diagnosed in cases when symptoms present>3 d postoperatively.Owing to its rarity,the risk factors for delayed neurological dysfunction are unclear.Consequently,this condition can result in irreversible neurological deficits and serious consequences.In this paper,we present a case of postoperative SEH that developed three days after hematoma evacuation.CASE SUMMARY A 68-year-old man with an American Spinal Injury Association(ASIA)grade C injury was admitted to our hospital with neck pain and tetraplegia following a fall.The C3-C7 posterior laminectomy and the lateral mass screw fixation surgery were performed on the tenth day.Postoperatively,the patient showed no changes in muscle strength or ASIA grade.The patient experienced neck pain and subcutaneous swelling on the third day postoperatively,his muscle strength decreased,and his ASIA score was grade A.Magnetic resonance imaging showed hypointense signals on T1 weighted image(T1WI)and T2WI located behind the epidural space,with spinal cord compression.Emergency surgical intervention for the hematoma was performed 12 h after onset.Although hypoproteinemia and pleural effusion did not improve in the perioperative period,the patient recovered to ASIA grade C on day 30 after surgery,and was transferred to a functional rehabilitation exercise unit.CONCLUSION This case shows that amelioration of low blood albumin and pleural effusion is an important aspect of the perioperative management of cervical surgery.Surgery to relieve the pressure on the spinal cord should be performed as soon as possible to decrease neurological disabilities.

Relaxed Stability Criteria for Time-Delay Systems:A Novel Quadratic Function Convex Approximation Approach

This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By introducing two adjustable parameters and two free variables,a novel convex function greater than or equal to the quadratic function is constructed,regardless of the sign of the coefficient in the quadratic term.The developed lemma can also be degenerated into the existing quadratic function negative-determination(QFND)lemma and relaxed QFND lemma respectively,by setting two adjustable parameters and two free variables as some particular values.Moreover,for a linear system with time-varying delays,a relaxed stability criterion is established via our developed lemma,together with the quivalent reciprocal combination technique and the Bessel-Legendre inequality.As a result,the conservatism can be reduced via the proposed approach in the context of constructing Lyapunov-Krasovskii functionals for the stability analysis of linear time-varying delay systems.Finally,the superiority of our results is illustrated through three numerical examples.

A NOTE ON THE GENERAL STABILIZATION OF DISCRETE FEEDBACK CONTROL FOR NON-AUTONOMOUS HYBRID NEUTRAL STOCHASTIC SYSTEMS WITH A DELAY

Discrete feedback control was designed to stabilize an unstable hybrid neutral stochastic differential delay system(HNSDDS) under a highly nonlinear constraint in the H_∞ and exponential forms.Nevertheless,the existing work just adapted to autonomous cases,and the obtained results were mainly on exponential stabilization.In comparison with autonomous cases,non-autonomous systems are of great interest and represent an important challenge.Accordingly,discrete feedback control has here been adjusted with a time factor to stabilize an unstable non-autonomous HNSDDS,in which new Lyapunov-Krasovskii functionals and some novel technologies are adopted.It should be noted,in particular,that the stabilization can be achieved not only in the routine H_∞ and exponential forms,but also the polynomial form and even a general form.

Primary frequency control considering communication delay for grid-connected offshore wind power systems

Offshore wind farms are becoming increasingly distant from onshore centralized control centers,and the communication delays between them inevitably introduce time delays in the measurement signal of the primary frequency control.This causes a deterioration in the performance of the primary frequency control and,in some cases,may even result in frequency instability within the power system.Therefore,a frequency response model that incorporates communication delays was established for power systems that integrate offshore wind power.The Padéapproximation was used to model the time delays,and a linearized frequency response model of the power system was derived to investigate the frequency stability under different time delays.The influences of the wind power proportion and frequency control parameters on the system frequency stability were explored.In addition,a Smith delay compensation control strategy was devised to mitigate the effects of communication delays on the system frequency dynamics.Finally,a power system incorporating offshore wind power was constructed using the MATLAB/Simulink platform.The simulation results demonstrate the effectiveness and robustness of the proposed delay compensation control strategy.

Adaptive predictor-based control for a helicopter system with input delays:Design and experiments

In this paper,we consider a 2-degrees-of-freedom(DOF)helicopter system subject to long input delays and uncertain system parameters.To address the challenges including unknown system parameters and input delays in control design,we develop an adaptive predictor-feedback control law to achieve trajectory tracking.Stability of the closed-loop system is further established,where the tracking errors are shown to converge towards zero.Through simulation and experiments on the helicopter system,we illustrate that tracking of a desired trajectory is achieved with the proposed control scheme.

Delayed Grafting as a Valid Technique in Burn Management: Experience from a Burn Unit in Oman

Background: Early excision and grafting has been the preferred method of managing major burns around the world since 1970. Considering the advances in health care and the development of new antibiotics over the past 50 years, delayed grafting as a technique for the management of burns over 15%-20% of total body surface area (TBSA) could have comparable results to that of early excision. This study aims to highlight the outcomes of practicing delayed grafting in burn patients. Methods: A case series analysis was performed of 51 patients who were admitted to the burns unit in Sultan Qaboos Hospital Salalah with over 20% TBSA between January 2014 and December 2019. The patients received prophylactic antibiotics and silver sulphadiazine dressing until the burn eschar had completely separated, followed by grafting. Results: Two patients were lost during the entire duration of the study. The mortality rate was comparable to that of early excision, while the rate of hypertrophic scarring was lower than the range reported by other studies. Conclusion: In the management of patients with over 20% TBSA, delayed grafting after complete separation of eschar is still a valid technique.

Stability of a Delayed Stochastic Epidemic COVID-19 Model with Vaccination and with Differential Susceptibility

In this paper, we treat the spread of COVID-19 using a delayed stochastic SVIRS (Susceptible, Infected, Recovered, Susceptible) epidemic model with a general incidence rate and differential susceptibility. We start with a deterministic model, then add random perturbations on the contact rate using white noise to obtain a stochastic model. We first show that the delayed stochastic differential equation that describes the model has a unique global positive solution for any positive initial value. Under the condition R0 ≤ 1, we prove the almost sure asymptotic stability of the disease-free equilibrium of the model.