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This work addresses the discrete-time containment control problem for first-order and second-order systems, incorporating position constraints, nonuniform time delays, and switching topologies. Projection operators are introduced to maintain agent states within the position constraints. Then, model transformation methods, along with stochastic properties of matrices, are employed to handle coupled nonlinearities stemming from position constraints and time delays. By using local information, distributed projection-based control schemes are proposed for multi-agent systems. Theoretical analysis shows that all followers ultimately converge into the convex hull spanned by leaders if the union of the communication topologies contains a directed spanning tree within each specified time interval. Finally, the theoretical results are verified by numerical simulations. • Containment control is studied for systems with constraints, delays, and switching. • A projection-based algorithm improves convergence to the leader-forming convex hull. • Model transformation is used to eliminate effects of non-uniform communication delays. • Numerical simulations validate the theoretical results. [ABSTRACT FROM AUTHOR]

This article addresses the real‐time reachable set problem on nonlinear time‐delay switched singular systems with state jump, which is subject to initial state and peak‐bound disturbance. Initially, based on the system state decomposition method, a state jump lemma is proposed, which combines the nonlinear function and the system state at the switching instant. Then, a real‐time bounded lemma is developed, premised on using the idea of average dwell‐time and analyzing subinterval function changes. Afterwards, the sufficient conditions for estimating the real‐time and nonreal‐time reachable set are established, which ensures that the reachable state of system can be restricted within a real‐time or nonreal‐time closed set. Finally, simulation results of the typical Direct Current boost chopper are performed to exhibit the effectiveness of the devised estimation scheme for the real‐time reachable set of system. [ABSTRACT FROM AUTHOR]

To meet the demand for estimating actuator and sensor faults simultaneously in a class of repetitive nonlinear time‐delay systems, this paper proposes a novel fault estimation strategy based on an iterative learning scheme. Firstly, an iterative‐learning‐based fault estimation law is designed to estimate actuator faults while system is free of sensor failures. Both the fixed initial shift and random one are taken into consideration. Secondly, a novel sensor fault observer is proposed based on an augmented state variable which consists of original system state and sensor fault signal; output compensation strategy is also provided to ensure the iterative‐learning‐based actuator fault estimation method is effective considering the existence of sensor failures. In addition, theorems based on λ$$ \lambda $$‐norm and linear matrix inequality are provided to determine values or ranges of gain matrices and parameters in proposed sensor fault observer and iterative‐learning‐based actuator fault estimation law. Finally, two simulation examples are provided to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

In current studies, non-integer order (NIO) plants with dead time have gained the significant attention of many researchers in the area of control theory. However, the design methods for fractional order controller tuning suffer from a lack of direct systematic tuning strategies due to a higher number of tuneable parameters. Most of the works on such design are optimisation-based whereas the analytical solutions are achieved with assumptions and approximations leading to compromised closed-loop robustness. This paper proposes a simple analytical design of a fractional-order tilt-integral-derivative (FOTID) controller for time-delayed NIO processes with a single tuneable parameter. Explicit tuning rules in terms of plant parameters are derived with user-defined stability margins. To prove the efficiency of the proposed control law, simulation comparisons with recently developed tuning rules are included. Lastly, the proposed control law is tested through experiments in a two-tank level loop for real-time validation. [ABSTRACT FROM AUTHOR]

Awareness plays a vital role in informing and educating people about infection risk during an outbreak and hence helps to reduce the epidemic's health burden by lowering the peak incidence. Therefore, this paper studies a susceptible-aware-infected-recovered (SAIR) epidemic model with the novel combinations of Michaelis-Menten functional type nonlinear incidence rates for unaware and aware susceptible with the inclusion of time delay as a latent period and a saturated treatment rate for infected people. The model is analyzed mathematically to describe disease transmission dynamics in two obtained equilibria: disease-free and endemic. We derive the basic reproduction number R 0 and investigate the local and global stability behavior of obtained equilibria for the time delay. A bifurcation analysis is performed using center manifold theory when there is no time delay, revealing the forward bifurcation when R 0 varies from unity. Moreover, the presence of Hopf bifurcation around EE is shown depending on the bifurcation parameter time delay. Lastly, the numerical simulations validate the analytical findings. [ABSTRACT FROM AUTHOR]

This paper studies the stability of stochastic nonlinear time‐delay systems with arbitrary switching and its application. A novel Krasovskii‐type stability theorem is introduced for stochastic nonlinear systems featuring arbitrary switching and time‐delay. Unlike previous results, this stability result removes the restriction that the infinitesimal generator of Lyapunov–Krasovskii functional (i.e., LV$$ \mathcal{L}V $$) must be negative definite and allows LV$$ \mathcal{L}V $$ to be indefinite. As an application, the tracking control is studied for a class of stochastic switched systems with inverse dynamics and time‐delay. The assumption condition imposed on the inverse dynamic subsystem is weaker compared with most of existing findings. Finally, we illustrate the feasibility and effectiveness of proposed control strategy by two simulation examples. [ABSTRACT FROM AUTHOR]

It is well accepted that fractional-order calculus yields a more accurate description of complex physical processes compared to integer-order one. So, fractional-order modelling is getting a good attention in the process industry. On the other hand, to meet design goals accurately, control designers prefer fractional-order controllers over integer-order ones due to the availability of more parameters. However, the design of such controllers are complex. More often, the design faces the challenge in real-time implementations, and the problem is circumvented by higher order approximations of fractional-order operators. In the presented work, three methods for integer-order Proportional–Integral–Derivative (PID) controller design are proposed based on Frequency Loop-Shaping (FLS) and Internal Model Control (IMC). To prove the efficacy of the presented control law, simulations are conducted and included along with a performance measure based on ISE (Integral of Square Error), ITAE (Integral of Time Absolute Error) and IAE (Integral of Absolute Error). [ABSTRACT FROM AUTHOR]

There exist infinite eigenvalues in singular vibration systems, which give rise to unstable responses and poor performances. The stability of singular vibration systems can be changed by eigenstructure assignment method. In this paper, partial eigenstructure assignment problems (PESAPs) and robust and minimum norm partial eigenstructure assignment problems for singular vibration systems with time-delay are studied. A necessary and sufficient condition is derived to solve PESAPs for singular vibration systems with time-delay. The parametric solution for PESAPs is given by the Moore-Penrose pseudoinverse method, and the algorithm for solving PESAPs is proposed. An optimization algorithm is developed to solve robust and minimum norm PESAPs. The algorithm can obtain the three types of optimal solutions, which is applicable to singular and nonsingular vibration systems with time-delay. The effectiveness of the proposed algorithms is verified by the results of two numerical examples. [ABSTRACT FROM AUTHOR]

Complex systems in the real world are characterized by multiple interactions among various components and often exhibit complexity, nonlinearity, or chaotic behavior. Signal complexity constitutes a pivotal attribute of nonlinear complex systems. Entropy-based methods for analyzing complexity offer a promising avenue for elucidating the dynamic behaviors inherent in such intricate systems. Diverging from multiscale approaches that primarily target low-frequency signal information, this study introduces Modified Hierarchical Time-delayed Distribution Entropy (MHTDE), a method that amalgamates the benefits of hierarchical analysis, time delay, and Distribution Entropy. This amalgamation facilitates the capture of complexity information spanning both high and low frequencies. Results from simulation experiments demonstrate the precision of MHTDE in quantifying signal complexity, showcasing its robustness to parameter variations and data length alterations. Furthermore, we employ MHTDE to extract complexity features from four real-life datasets and employ the K-Nearest Neighbor algorithm for classification. The classification performance of MHTDE outperforming baseline models. Consequently, the proposed MHTDE method underscores its competence in efficacious feature extraction. [ABSTRACT FROM AUTHOR]

Communication plays a pivotal role in distributed optimization problems, where unavoidable communication delays are presented. This research studies the distributed constrained optimization problem concerning second‐order multi‐agent systems with double‐integrator under time‐varying communication delays. An adaptive distributed optimization algorithm using multi‐agent system consensus technique and Karush–Kuhn–Tucker conditions is developed to deal with this problem. The local constraint term is solved adaptively through local dual Lagrange multipliers. When the cost function is strongly convex, and the communication topology is undirected and connected, we employ the Lasalle invariance principle to analyze the delay effects on convergence analysis. Moreover, we give an upper bound on communication delay. Finally, the provided numerical simulation examples demonstrate that the developed method is robust for the limited communication delay and the derived results are conservative. [ABSTRACT FROM AUTHOR]

This paper proposes a simple but effective method for constructing the state feedback controller to solve the exponential stabilization problem for a class of feedforward nonlinear systems subject to different time-delay states. The form of state feedback controller, which depends on a positive parameter to be determined, is firstly presented. And then, by considering the Lyapunov-Krasovskii functional with exponential term and taking the appropriate positive parameter, the state feedback controller is achieved to ensure the exponential stability of the closed-loop system. Finally, the proposed design scheme is utilized to the control design of resonant circuit system. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of SIR model with time-delay and evolutionary effects under the homogeneous Neumann boundary conditions. Firstly, the stability of the positive equilibrium point is analyzed with time delay as the parameter, and the existence condition of Hopf bifurcation is given. Secondly, the bifurcation direction and the stability of periodic solutions are given by using the theory of normal form and center manifold. Finally, Matlab was used for the numerical simulation to verify the correctness of the conclusion, and it is concluded that the time delay will make the stable system become unstable and generate Hopf bifurcation. [ABSTRACT FROM AUTHOR]

Summary: Radio frequency identification device (RFID) has emerged as one of the most potential building blocks for future IoT‐enabled technologies. Various applications like logistic monitoring use the RFID system to deal with the tagged objects. RFID‐based tracking approach is extremely solicited for appropriate logistic distribution because of the frequent tagged‐objects rearrangements. Nevertheless, with an RFID system, one of the most significant issues is resolving collisions between tags as they transfer data to the reader at the same time. This work investigates the core issue of locating all lost tags in RFID systems. The most significant factor in missing tag recognition is to reduce the time required for execution. A problem needs to be formulated to differentiate the tagged objects' motion state, that is, static or dynamic, to handle this issue. It tracks the moving objects with various existing localization approaches. Finally, a tag detection known as constructive Steiner graph matching (CSGM) detection is proposed to achieve time efficiency by utilizing RFID collision signals. Specifically, the physical‐layer features are considered for differentiating the positions. Experimental outcomes demonstrate that the anticipated model can attain better prediction accuracy by reducing inventory time compared to other approaches. Simulation findings show that the suggested approach performs exceptionally well in giving a significant performance boost in an RFID system. It minimizes the complexity of tracking the objects. The simulation outcomes illustrate that the algorithm's identification speed is substantially enhanced and ensuring high system efficiency. The simulation results of the proposed algorithm have been improved in terms of system efficiency (9.5%), success rate (6.3%), and identification speed (4%) compared to the conventional algorithm. The suggested CSGM technique's average waiting time is decreased by more than 45.372%, and its detection speed is increased by at least 38.219% compared to other existing algorithms. [ABSTRACT FROM AUTHOR]

This paper is concerned with the linear delayed forward–backward stochastic differential equations (D-FBSDEs). The existence of time delay leads to the infinite-dimensional problem which makes the explicit solvability more challenging. The main contribution is to propose a discretisation approach which gives the explicit solution of the D-FBSDEs and consists of the following three steps: first, we transform the continuous-time D-FBSDEs into the discrete-time form with the aid of interval partition. Second, we derive the solution of the discrete-time D-FBSDEs by applying backward iterative induction. Finally the explicit solution of the continuous-time D-FBSDEs is obtained by taking the limit to the solution of discrete-time form which is also strictly proved under continuous-time framework. The proposed approach is applicable for more general FBSDEs with delay, which would provide a complete solution to the stochastic LQ control with time delay. [ABSTRACT FROM AUTHOR]

We study stabilization of linear uncertain systems under unknown control directions using a bounded extremum seeking controller in the presence of a small time‐varying measurement delay. We assume that the measurements are subject to discontinuous disturbances. The main novelty is that these disturbances possess not only the constant part as in the existing results, but also small discontinuous part that may appear due to quantization. We consider two types of measurements: the state measurements and the state quadratic norm ones. In the latter case the constant part of the disturbances may be arbitrary large. By using the recently proposed time‐delay approach to Lie‐brackets‐based averaging, we transform the closed‐loop system to a time‐delay (neutral type) one with no terms depending on the disturbance derivative, which has a form of perturbed Lie brackets system. The input‐to‐state stability (ISS) of the time‐delay system guarantees the same for the original one. We further transform the neutral system to an ordinary differential equation (ODE) with delayed perturbations and employ variation of constants formula leading to explicit conditions in terms of simple inequalities with less conservative results in the most of numerical examples. Two numerical examples are provided to illustrate the efficiency of the method. [ABSTRACT FROM AUTHOR]

Summary: This paper proposes a hybrid observer for state estimation over a network. The network provides delayed measurements of the output of the plant at time instants that are not necessarily periodic and are accompanied by timestamps provided by a clock that synchronizes with the clock of the observer in finite time. The proposed observer, along with the plant and communication network, are modeled by a hybrid dynamical system that has two timers, a logic variable, and two memory states to capture the mechanisms involved in the events associated with sampling and arrival of information, as well as the logic in the estimation algorithm. The hybrid model also includes a generic clock synchronization scheme to cope with a mismatch between the clocks at the plant and the observer. Convergence properties of the estimation error of the system are shown analytically and supported by numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, the $ H_{\infty } $ H ∞ consensus problem of stochastic nonlinear multi-agent systems with time-delay, Markov jump and $ (x, u, v) $ (x , u , v) -dependent noises is studied. Firstly, the $ H_{\infty } $ H ∞ consensus problem is transformed into a standard $ H_{\infty } $ H ∞ control problem by model transformation. Then, a dynamic output feedback control protocol is constructed by solving a set of linear matrix inequalities to ensure that the closed-loop system achieves the mean square consensus and meets the specified $ H_{\infty } $ H ∞ performance level. After that, both delay-independent and delay-dependent stochastic bounded real lemmas are established by taking advantage of the Lyapunov–Krasovskii function method and the generalised It $ \hat {\rm {o}} $ o ^ formula. Finally, we illustrate the validity of the developed method with numerical simulations. [ABSTRACT FROM AUTHOR]

Based on nonlinear memory feedback, the robust admissibility problem of a class of singular nonlinear time-delay systems was investigated. First, an equivalent structural model of the system was created using the state decomposition approach. Then, sufficient criteria for the robust admissibility of the system were obtained in the form of linear matrix inequalities using the Lyapunov–Krasovskii theory and free weighted matrix method. Subsequently, the closed-loop robust admissibility of the system under nonlinear memory feedback control was investigated using similar research techniques as before, yielding corresponding results. The intended design controller was obtained by explicitly computing each component in the deconstructed structure of the nonlinear memory feedback controller. Importantly, the flexibility and viability of the planned control design could be enhanced by the algorithm for solving controller gain through this component decomposition. Finally, numerical examples confirmed the feasibility of the method. [ABSTRACT FROM AUTHOR]

This research studies the stabilization of the linear KdV equation with time-delay on boundary feedback in the presence of a saturated source term. Under certain hypotheses, the proof of well-posedness is established. The result of exponential stability is demonstrated using an appropriate Lyapunov functional. [ABSTRACT FROM AUTHOR]

In this paper, the fixed/prescribed-time stability issues were considered for stochastic systems with time delay. First, some new fixed-time stability and prescribed-time stability criteria for stochastic systems with delay and multi-delay were established. Second, based on the new fixed/prescribed stability criteria, the fixed-time stabilization of the stochastic system with time-delay and the prescribed-time stabilization of the stochastic reaction-diffusion system with multi-delay were investigated, respectively. Third, two new fixed/prescribed-time delay-independent control mechanisms were designed. The primary advantage of the innovative fixed/prescribed-time controller lies in its independence from delayed states. This makes the controller applicable to systems with unknown delays. Finally, three numerical examples were provided to illustrate the feasibility of the stated theoretical results.

This study focuses on designing PI controllers for time-delay systems using various model order reduction techniques to reduce complexity. The stability boundary locus method was used to determine PI parameters that stabilizing reduced order models. After the PI parameters have been determined using the weighted geometric center method, the calculated controller parameters have been implemented in the original system. In this way, the efficiency of the controller design is effectively demonstrated through the reduction techniques. In addition, the study investigated the effectiveness of reduction methods with increasing time delay and adding an integrator to the system. The importance of these results is that they demonstrate the use of model order reduction techniques in the design of controllers for time-delay systems and reveal the advantages of these methods.

The increasing penetration of renewable energy sources in power systems presents frequency stability challenges, as power electronic-connected sources like photovoltaics and batteries inherently provide limited inertia and damping for frequency regulation. To address this issue, this paper proposes a distributed cooperative control method for secondary frequency regulation. Additionally, it achieves economic dispatch among generators and proportional power sharing among renewable energy sources. The proposed control system enables photovoltaics and battery energy storage systems to actively manage frequency in conjunction with power generators. It operates using a sparse communication network that mirrors the topology of the power network. Moreover, the cooperative control method can tolerate communication time delays while maintaining a stable frequency response. The frequency stability of the proposed control system, both with and without time delays, is assured through Lyapunov methods and eigenvalue analysis. Validation is performed on a modified IEEE 14-bus system with integrated photovoltaics and batteries, demonstrating the efficacy of the proposed secondary frequency control.

The satellite bears complex vibration loads transmitted from the satellite-rocket interface during launch, where medium–high frequency and small amplitude vibration is highly likely to harm the satellite's internal precision instruments. Under such special conditions, the time-delay factor of the MR damper as the actuator cannot be ignored in the vibration control of the magnetorheological (MR) whole-spacecraft. To compensate actuator time-delay, and consider the system's nonlinear characteristics under medium–high frequency and small amplitude conditions, a gray prediction time-delay compensation method is proposed based on the human-simulated intelligent controller (HSIC). After verifying through simulation and experiment that actuator time-delay affects the vibration response of the MR whole-spacecraft, the HSIC based on gray prediction is designed. Then, the control effect of HSIC with or without time-delay is simulated numerically. The results reveal that after considering the time-delay factor, the resonance peak increases by 17%, and the transmissibility of the concerned particularly frequency band (40 Hz) increases by 62%, which implies a significant deterioration in the control effect. Following, to make up for the response deterioration caused by the time-delay, the HSIC based on gray prediction is used for numerical simulation. The results confirm that reasonable time-delay compensation can effectively improve the system dynamics. This study provides a reference for the practical application of the whole-spacecraft controller. [ABSTRACT FROM AUTHOR]

In this brief communication, we highlight several critical inaccuracies in the paper entitled "A novel methodology for a time-delayed controller to prevent nonlinear system oscillations," identified by the DOI: 10.1177/14613484231195276. The core of the non-perturbative approach discussed in this paper is the introduction of a trial solution with an indeterminate nonlinear frequency. We elucidate the technical missteps and provide necessary corrections. The scrutinized article presents ample opportunities for enhancement, and we propose several amendments. Additionally, we reveal that the numerical outcomes showcased in the mentioned paper expose deficiencies in the proposed approximate solution. With the amendments implemented herein, a more precise numerical solution is achieved. [ABSTRACT FROM AUTHOR]

This article studies the output feedback H∞$$ H\infty $$ control problem for event‐triggered Markovian jump networked control systems with signal quantization. First, a Lyapunov–Krasovskii function is constructed, which contains time delay, upper bound of time delay and conditional transition probability information of Markovian jump systems. Second, when using the Wirtinger's inequality and the Reciprocally convex inequality to estimate the upper bound of the delay of the weak infinitesimal generator operator of the Lyapunov–Krasovskii function, the event‐triggered scheme and the signal quantization scheme are introduced. Finally, the stability criterion of the closed‐loop system of event‐triggered Markovian jump networked control systems and the design method of the output feedback controller of H∞$$ H\infty $$ disturbance attenuation level γ$$ \gamma $$ are given in the form of linear matrix inequalities (LMIs). The effectiveness of the proposed method is verified by two numerical examples. [ABSTRACT FROM AUTHOR]

The optimal control issue of discrete‐time nonlinear unknown systems with time‐delay control input is the focus of this work. In order to reduce communication costs, a reinforcement learning‐based event‐triggered controller is proposed. By applying the proposed control method, closed‐loop system's asymptotic stability is demonstrated, and a maximum upper bound for the infinite‐horizon performance index can be calculated beforehand. The event‐triggered condition requires the next time state information. In an effort to forecast the next state and achieve optimal control, three neural networks (NNs) are introduced and used to approximate system state, value function, and optimal control. Additionally, a M NN is utilized to cope with the time‐delay term of control input. Moreover, taking the estimation errors of NNs into account, the uniformly ultimately boundedness of state and NNs weight estimation errors can be guaranteed. Ultimately, the validity of proposed approach is illustrated by simulations. [ABSTRACT FROM AUTHOR]

Considering the time delay originating from a certain incubation period or asymptomatic state, we propose a delayed epidemic system within the noisy environment of the hepatitis B virus to analyze the mechanism of disease transmission and elucidate how to control it by applying the strategy of vaccinating and treatment. Applying stochastic Lyapunov functional theory, we first construct an integral Lyapunov function coupling the time delay and stochastic fluctuation to investigate whether there exists a unique global solution to the model. Next, we yield the threshold condition for controlling disease extinction, and persistence, as well as its stationary distribution. Governed by these sufficient conditions, we study the existence of optimal control solutions in deterministic and stochastic scenarios to uncover how to accelerate disease extinction through vaccination and treatment. The results indicate that the time delay will prolong the duration of the disease for the original system but suppress the peak value of HBV in the controlled system. Finally, we verify the versatility of theoretical results by numerical simulations. These results will effectively decipher the importance of the time delay in the control of hepatitis B. [ABSTRACT FROM AUTHOR]

To improve the ride comfort of the vehicle and the high-efficiency control requirements of the suspension, this paper proposes a time-delay control strategy and the idea of using a linear motor as the actuator. This paper analyses the damping characteristics of the time-delay control strategy in the time domain and frequency domains. A linear equivalent excitation method is proposed to optimise the optimal time-delay control parameters under complex excitations. The stability of the system is analysed. The damping effect of time-delay control active suspension is verified by numerical simulation. An experimental hardware platform of a linear motor and active suspension was built further to verify the effectiveness of the time-delay control strategy. The experimental results show that the relative errors of root mean square values of experimental and simulation results are within 16% under each working condition. The experimental results verify the effectiveness of the simulation results. [ABSTRACT FROM AUTHOR]

This paper studies residual evaluation of fault detection in discrete‐time systems considering unknown‐but‐bounded disturbance. By applying Lyapunov stability principle and zonotopic technique, respectively, two dynamic threshold estimation methods are proposed to detect fault of discrete‐time systems. The proposed methods are extended to systems with time‐delay to improve the applicability in practical systems. The effectiveness and comparison of the proposed methods are illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

The purpose of this manuscript is to analyze the bifurcation of the tri-rhythmic model with three stable limit cycles under the excitation of Gaussian colored noise, which aims to reveal the extremely complex nonlinear dynamics in biology. In the deterministic bifurcation of the tri-rhythmic model with time-delay, an interesting tri-rhythmic collapse and recovery phenomenon is found. By tuning the time-delay feedback, the model also exhibits a switch between tri-rhythmic and bi-rhythmic behavior. Furthermore, the tri-rhythmic model under colored noise excitation is discussed theoretically based on the stationary probability density function obtained by the stochastic averaging method. The variation in the number of peak values of the stationary probability density function is observed, thereupon enabling the stochastic bifurcation of the tri-rhythmic oscillator. Therefore, by adjusting the time-delay feedback and colored noise, many abundant bifurcation phenomena can be acquired. The theoretical analysis is consistent with the results of the dynamic numerical simulation. Our study may provide a new perspective for further exploring the bifurcation phenomenon of the tri-rhythmic model, which has important practical significance. [ABSTRACT FROM AUTHOR]

In this paper, a delayed discrete Mittag-Leffler matrix function generated by two noncommutative square matrices is introduced. Utilizing this function, the paper establishes an explicit expression for solving constant delay fractional difference systems. Additionally, a criterion for determining the Ulam-Hyers stability of delay fractional difference systems with constant coefficients is derived using the aforementioned explicit representation formula. [ABSTRACT FROM AUTHOR]

In this article, the topic of event-triggered H∞ control is investigated for a singular networked cascade control system (SNCCS) under periodic DoS attacks, norm-bounded uncertainty, and external disturbances. Unlike existing articles, the SNCCS is assumed to be singular not only in the inner loop but also in the outer loop. Then, using Multiple Lyapunov Functionals (MLF), new sufficient conditions are derived for the admissibility of the SNCCS through linear matrix inequalities, guaranteeing the regularity and impulse-freeness of the system. Afterward, state-feedback controllers are designed for both the inner and the outer loops of the system. All the derived theories in this article can be utilized for stabilizing both singular and non-singular NCCSs. Finally, simulation results are presented on a steam generation process in a power plant to validate the proposed method.

This paper addresses the stabilization of a general class of linear single-input/single-output (SISO) second-order non-minimum phase systems with input channel delays using Proportional-Integral (PI) controllers. Such systems arise in various applications, including power electronic circuits and biochemical reactors. The primary goal is to enhance system performance by determining optimal control gains that shift the spectral abscissa of the closed-loop system as far to the left as possible, thereby improving its decay rate. To achieve this, we introduce a geometric framework that characterizes the stability region of the closed-loop system in three distinct cases. Our main contribution is a systematic tuning approach to achieve the desired decay rate when feasible. Additionally, we discuss the controller’s fragility and the delay margin of the closed-loop system to ensure practical applicability. The effectiveness of the proposed method is demonstrated through numerical simulations for each scenario. Finally, two practical case studies—a boiler steam drum and a DC-DC boost converter—are presented to illustrate the results’ relevance in practice.

Magnetorheological (MR) dampers possess the ability to alter the damping force of the damper by modifying the viscosity of Magnetorheological Fluid (MRF). The prevalent MR dampers mostly feature a single damping channel structure, which necessitates adjusting the magnetic field strength to attain asymmetric damping force during the compression and recovery stroke. However, it amplifies the influence of the control circuit’s time-delay on damping force. This article proposes the design of a dual-damping-channel MR damper to structurally achieve the asymmetric damping force. The dimensions of key components were determined using damping calculation formulas and electromagnetic simulation. A prototype MR damper was manufactured, and experimental verification was conducted. The results indicate that the damper operates optimally, and the damping force value and adjustable range of damping force meet the design objectives. The indicator characteristic curve of the shock absorber shows that the MR shock absorber designed in this paper can effectively reduce the influence of MRF time-delay on the damping force value of the shock absorber.

The performance of an optoelectronic reservoir computing (RC) system for recognizing apple leaf diseases is numerically investigated. The disease spot feature extraction and selection methods suitable for time-delay RC are investigated. Two masking methods of sequence extension masking and matrix transformation masking are examined, with appropriate parameters, the optoelectronic RC achieves minimum errors of 0.01 and 0.03 under sequence extension masking and matrix masking methods, respectively. The nonlinear dynamics of the optoelectronic reservoir in the absence of data injection are compared with its recognition performance to establish the relationship between recognition capabilities and the system’s nonlinear dynamics. Additionally, we compared the recognition errors of optoelectronic RC, linear RC, and k-nearest neighbor algorithms. It illustrates that optoelectronic RC, under the nonlinear transformation of the Mach-Zehnder Modulator (MZM) and delayed feedback, can map input information nonlinearly to a high-dimensional state space, enabling effective classification along linear hyperplanes in this high-dimensional space.

The paper investigates the nonlinear transversal vibrations of a cantilever beam structure in the primary resonance case. A time-delayed position-velocity control is suggested to reduce the nonlinear vibrations of the structure under consideration. A non-perturbative method (NPM) is used to get an equivalent analogous linear differential equation (DE) to the original nonlinear one. For the benefit of the readers, a comprehensive description of the NPM method is provided. The theoretical findings are validated through a numerical comparison carried out by employed the Mathematica Software. Both the numerical solutions and the theoretical outcomes showed excellent agreement. As well-known, all classic perturbation techniques use Taylor expansion, when the restoring forces are present, to expand these forces and therefore lessen the difficulty of the given problem. Under the NPM, this weakness is no longer present. Furthermore, one may examine the stability examination of the issue with the NPM something that was not possible with prior traditional techniques. The controlled linear equivalent model is examined using the multiple-scales homotopy method. The amplitude-phase modulation equations which control the dynamics of the structure at the various resonance circumstances are established. The loop-delay stability diagrams are analyzed. It is looked at how the different controller parameters impact the oscillation behaviors of the system. The obtained theoretical outcomes showed that the loop delay has an important impact on the effectiveness of the control. Therefore, the ideal loop-delay values are given and used to develop the enactment of the organized control. The completed analytical results are also numerically validated, to reveal their good correlation with the achieved theoretical new results. [ABSTRACT FROM AUTHOR]

The excellent performance of the controller and its insensitivity to time-delay are very important for active suspension. In this paper, a novel output-feedback H∞ optimal controller is designed for half-vehicle suspension system and it performs better than the common output-feedback H∞ optimal controller. To further study the effect of time-delay on the performance of the controller, a visual modeling and simulation method is proposed, and the detailed modeling process is given. The influence of time-delay on the vertical acceleration and pitching acceleration of vehicle body is simulated under bump road excitation and C-class pavement excitation, respectively. The results show that when the time-delay is less than 25 ms, the performance of the controller is little affected under the bump road, and under the C-level road excitation, even if the time-delay reaches 50 ms, the performance of the controller will not be affected. [ABSTRACT FROM AUTHOR]

Controllability of nonlinear delayed leader–follower multi-agent system with fixed communication topology is introduced. A solution of a semilinear time-delay control system and Gramian matrix for the linear part which has Kronecker delay perturbation of exponential matrix function are given. The assumptions and conditions under which the nonlinear delay multi-agent system can be controlled are determined thanks to control problem into fixed point problem. A comprehensive example to illustrate given theoretical contents is presented. [ABSTRACT FROM AUTHOR]

This paper investigates reachable set estimation and state-feedback controller design for linear time-delay control systems with bounded disturbances. By constructing an appropriate Lyapunov–Krasovskii functional, we obtain a delay-dependent condition, which determines the admissible bounding ellipsoid for the reachable set of the system we considered. Then, a sufficient condition in the form of liner matrix inequalities is given to solve the problem of controller design and reachable set estimation. Then, by minimizing the volume of the ellipsoid and solving the liner matrix inequality, we obtain the desired ellipsoid and controller gain. A comparative numerical example is given to show the effectiveness of our result. [ABSTRACT FROM AUTHOR]

The focus of this article is to design a distributed preview tracking controller for a class of nonlinear interconnected systems with time‐delay. By constructing the error systems with the information of previewable reference signal, and defining an H∞$$ {H}_{\infty } $$ performance index, the original preview tracking problem is converted into the H∞$$ {H}_{\infty } $$ control problem of the error system. Based on the relationship between the interconnection matrices and the input matrices, a distributed controller using not only the local state vector information but also the interconnection term information is designed for the error systems. Under this controller, the closed‐loop error system is decoupled. With the help of Lyapunov‐Krasovskii functional, the sufficient conditions, the asymptotic stability of the closed‐loop error system with H∞$$ {H}_{\infty } $$ disturbance attenuation level, are established. The distributed preview tracking controller, which is composed of state feedback, integrator, and preview feedforward, is acquired by integrating the controller of the error system. The proposed preview controller is applied to the chemical reactor recycles system and double‐parallel inverted pendulum system. The simulation verify that this controller is very effective in improving the tracking performance. [ABSTRACT FROM AUTHOR]

The present article focuses on the new meticulous model based on the postulate of memory-dependent derivatives to analyze the thermo-mechanical interactions inside the nano-beam-based machined resonators. Also, the size effect on dynamic responses of thermoelastic vibrations of homogeneous and isotropic nano-beam is considered. The fundamental expressions are formulated in the frame of non-local generalized thermoelasticity with paired relaxation times by operating the results of Euler-Bernoulli beam theory, non-local effect, and memory-dependent derivative. The proposed model is applied to study the nano-beam-based machined resonator subjected to the ramp-type heating and exponentially decaying time-dependent load. Closed-form solutions of the physical fields are examined by applying the Laplace transform mathematical mechanism. However, the coherence of the new thermal conductivity framework, a collation has been bestowed among the results obtained in the presence or absence of the memory-dependent derivative; also, the size effect is analyzed on the significant parameters of nano-beam such as deflection, temperature, displacement as well as bending moment. Moreover, the prominent influence of the distinct affecting parameters such as constituents of memory-dependent derivative (kernel function and time delay) and ramping time parameter with an applied load on the physical fields have been investigated with the help of quantitative results. [ABSTRACT FROM AUTHOR]

This study focuses on designing PI controllers for time-delay systems using various model order reduction techniques to reduce complexity. The stability boundary locus method was used to determine PI parameters that stabilizing reduced order models. After the PI parameters have been determined using the weighted geometric center method, the calculated controller parameters have been implemented in the original system. In this way, the efficiency of the controller design is effectively demonstrated through the reduction techniques. In addition, the study investigated the effectiveness of reduction methods with increasing time delay and adding an integrator to the system. The importance of these results is that they demonstrate the use of model order reduction techniques in the design of controllers for time-delay systems and reveal the advantages of these methods. [ABSTRACT FROM AUTHOR]

Time-delay effect and bifurcation phenomenon are important topics in the study of reaction–diffusion equations. In this paper, we consider a three-species predator–prey system with diffusion and incubation delay for predator. The stability and Hopf bifurcation are mainly discussed. We conclude that there exists a critical value of delay, such that the internal equilibrium is stable or unstable as the delay crosses the critical value. Especially, the system emerges Hopf bifurcation phenomenon at this critical value. For bifurcation solution, the conclusions of stability, period and bifurcation direction are also presented. Additionally, numerical simulations are proceeded to support the main results. In biology, the existence of bifurcation solution means that when the delay of predator reaches to a certain extent, the predator and prey will coexist within a period of time. It turns out that the related computations and analyses are much more complicated than that of two-species time-delay systems.

State-of-art power systems are progressing rapidly due to the advent of converter-interfaced power generation. Power system stabilizers are commonly employed in synchronous generators to damp low-frequency oscillations. However, many of these generators have been decommissioned by converter-interfaced generations. This means that converter-interface-based wind and solar power plants should also commit to oscillation damping. In addition, renewable generators may be coordinated with power system stabilizers to enhance the damping. This paper recommended a new advanced design of damping control system using wide-area signal with converter-interfaced generations. The major contribution of this work is to improve the damping of low-frequency oscillations while keeping the frequency in the specified range taking into account renewable energy sources. This paper introduced a mixed H2/H∞ using non-convex optimization utilized to design damping controllers for renewable integrated power systems to secure system operation against low-frequency oscillation modes. This multi-objective control design permits for more reliable and precise specification of the recommendable closed-loop behavior. The proposed robust controller is tested on grid-forming wind turbine type-III DFIGs and generic dynamic PV plants integrated large study power systems, whereas robustness is evaluated against several perturbations and communication delay through dynamic simulation.

This paper introduces a mathematical model that simulates the transmission of the dengue virus in a population over time. The model takes into account aspects such as delays in transmission, the impact of inhibitory effects, the loss of immunity, and the presence of partial immunity. The model has been verified to ensure the positivity and boundedness. The basic reproduction number R0 of the model is derived using the advanced next-generation matrix approach. An analysis is conducted on the stability criteria of the model, and equilibrium points are investigated. Under appropriate circumstances, it was shown that there is local stability in both the virus-free equilibrium and the endemic equilibrium points when there is a delay. Analyzing the global asymptotic stability of equilibrium points is done by using the appropriate Lyapunov function. In addition, the model exhibits a backward bifurcation, in which the virus-free equilibrium coexists with a stable endemic equilibrium. By using a sensitivity analysis technique, it has been shown that some factors have a substantial influence on the behavior of the model. The research adeptly elucidates the ramifications of its results by effortlessly validating theoretical concepts with numerical examples and simulations. Furthermore, our research revealed that augmenting the rate of inhibition on infected vectors and people leads to a reduction in the equilibrium point, suggesting the presence of an endemic state.

Abstract This work presents a control approach based on sliding-mode-control (SMC) to design robust $$H_{\infty }$$ H ∞ state feedback controllers for load frequency regulation of delayed interconnected power system (IPS) with parametric uncertainties. Considering both state feedback control strategy and delayed feedback control strategy, two SMC laws are proposed. The proposed control laws are designed to improve the stability and disturbance rejection performance of delayed IPS, while stabilization criteria in the form of linear matrix inequality are derived by choosing a Lyapunov–Krasovskii functional. An artificial time-delay is incorporated in the control law design of the delayed feedback control structure to enhance the controller performance. A numerical example is considered to study the control performance of the proposed controllers and simulation results are provided to observe the dynamic response of the IPS.