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This paper aims to use a new design approach based on a Lagrange mean value theorem for the stabilization of multivariable input‐delayed system by linear controller.

The delay‐dependent asymptotical stability conditions are derived by using augmented Lyapunov‐Krasovskii functionals and formulated in terms of conventional Lyapunov matrix equations and some simple matrix inequalities. Proposed design approach is extended to robust stabilization of multi‐variable input‐delayed systems with unmatched parameter uncertainties. The maximum upper bound of delay size is computed by using a simple optimization algorithm.

A liquid monopropellant rocket motor with a pressure feeding system is considered as a numerical design example. Design example shows the effectiveness of the proposed design approach.

The proposed approach can be used in the analysis and design of the uncertain multivariable time‐delay systems.

The paper has a great potential in the stability analysis of time‐delay systems and design of time‐delay controllers and may openup a new direction in this area.

The purpose of this paper is with delay-independent stabilization of nonlinear systems with multiple time-delays and its application in chaos synchronization of Rössler system.

Based on linear matrix inequality and algebra Riccati matrix equation, the stabilization result is derived to guarantee asymptotically stable and applicated in chaos synchronization of Rössler chaotic system with multiple time-delays.

A controller is designed and added to the nonlinear system with multiple time-delays. The stability of the nonlinear system at its zero equilibrium point is guaranteed by applying the appropriate controller signal based on linear matrix inequality and algebra Riccati matrix equation scheme. Another effective controller is also designed for the global asymptotic synchronization on the Rössler system based on the structure of delay-independent stabilization of nonlinear systems with multiple time-delays. Numerical simulations are demonstrated to verify the effectiveness of the proposed controller scheme.

The introduced approach is interesting for delay-independent stabilization of nonlinear systems with multiple time-delays and its application in chaos synchronization of Rössler system.

This paper aims to investigate the fast attitude coordinated control problem for rigid satellite swarms with communication delays.

Based on behavior‐based control approach, the attitude control system is designed to guarantee that the attitude of the satellite swarm converge to a dynamic reference state in finite time. A fast sliding mode is developed to improve the convergence rate and robustness of the control system. All the effects of communication delays, parameter uncertainties and external disturbances are taken into account simultaneously, and the communication topology of the satellite swarm can be arbitrary types. Numerical simulations are provided to demonstrate the analytic results.

Despite the existence of communication delays, parameter uncertainties and external disturbances, the stability of the closed‐loop system can be successfully guaranteed and the proposed control strategies are effective to overcome these unexpected phenomena subject to arbitrary communication topology.

This paper introduces a fast terminal sliding mode control method which can guarantee the fast convergence of the attitude state of the satellite swarm in the presence of communication delays, switched communication topology, parameter uncertainties and external disturbances.

Rapid satellite capture by a free-floating space robot is a challenge problem because of no-fixed base and time-delay issues. This paper aims to present a modified target capturing control scheme for improving the control performance.

For handling such control problem including time delay, the modified scheme is achieved by adding a delay calibration algorithm into the visual servoing loop. To identify end-effector motions in real time, a motion predictor is developed by partly linearizing the space robot kinematics equation. By this approach, only ground-fixed robot kinematics are involved in the predicting computation excluding the complex space robot kinematics calculations. With the newly developed predictor, a delay compensator is designed to take error control into account. For determining the compensation parameters, the asymptotic stability condition of the proposed compensation algorithm is also presented.

The proposed method is conducted by a credible three-dimensional ground experimental system, and the experimental results illustrate the effectiveness of the proposed method.

Because the delayed camera signals are compensated with only ground-fixed robot kinematics, this proposed satellite capturing scheme is particularly suitable for commercial on-orbit services with cheaper on-board computers.

This paper is original as an attempt trying to compensate the time delay by taking both space robot motion predictions and compensation error control into consideration and is valuable for rapid and accurate satellite capture tasks.

This paper explains the development of a dispatch reliability prediction method for passenger aircraft. The method provides an objective means of assessing the delay rate for aircraft systems in the very early stages of aircraft design, leading to the minimisation of subsequent corrective actions, and thus reducing operating cost. The method encompasses two models: one each for short‐haul and long‐haul aircraft. It uses delay rate data and design/performance parameters to derive statistical equations, one set for each aircraft system. These equations relate the delay rate for a particular system to selected design/performance parameters. The models give high predictability and can be applied at the conceptual design phase, using the minimum amount of input data.

The purpose of this paper is to introduce an auxiliary parameter into the well‐known variational iteration algorithm which proves very effective to control the convergence region of approximate solution.

In this paper, an auxiliary parameter is introduced into the well‐known variational iteration algorithm which proves very effective to control the convergence region of approximate solution.

The present technology provides a simple way to adjust and control the convergence region of approximate solution for any values. An optimal auxiliary parameter can be obtained by the error of norm two of the residual function.

It is confirmed that submitted manuscript is original and is not being considered in any other journal.

In this article, the authors aims to introduce a novel Vieta–Lucas wavelets method by generalizing the Vieta–Lucas polynomials for the numerical solutions of fractional linear and non-linear delay differential equations on semi-infinite interval.

The authors have worked on the development of the operational matrices for the Vieta–Lucas wavelets and their Riemann–Liouville fractional integral, and these matrices are successfully utilized for the solution of fractional linear and non-linear delay differential equations on semi-infinite interval. The method which authors have introduced in the current paper utilizes the operational matrices of Vieta–Lucas wavelets to converts the fractional delay differential equations (FDDEs) into a system of algebraic equations. For non-linear FDDE, the authors utilize the quasilinearization technique in conjunction with the Vieta–Lucas wavelets method.

The purpose of utilizing the new operational matrices is to make the method more efficient, because the operational matrices contains many zero entries. Authors have worked out on both error and convergence analysis of the present method. Procedure of implementation for FDDE is also provided. Furthermore, numerical simulations are provided to illustrate the reliability and accuracy of the method.

Many engineers or scientist can utilize the present method for solving their ordinary or Caputo–fractional differential models. To the best of authors’ knowledge, the present work has not been used or introduced for the considered type of differential equations.

The purpose of this study is an application of the multi-wavelets Galerkin method to delay differential equations with vanishing delay known as Pantograph equation.

The method consists of expanding the required approximate solution at the elements of the Alpert multi-wavelets. Using the operational matrices of integration and wavelet transform matrix, the authors reduce the problem to a set of algebraic equations.

Because of the large size of the system, thresholding is used to obtain a new sparse system, and then this new system is solved to reduce the computational effort and related computer run time. The authors demonstrate that the solutions may be efficiently represented in a multi-wavelets basis because of flexible vanishing moments property of this type of multi-wavelets.

The L₂ convergence of the scheme for the proposed equation has been investigated. A series of numerical tests is provided to demonstrate the validity and applicability of the technique.

The purpose of this study is to develop stable, convergent and accurate numerical method for solving singularly perturbed differential equations having both small and large delay.

This study introduces a fitted nonpolynomial spline method for singularly perturbed differential equations having both small and large delay. The numerical scheme is developed on uniform mesh using fitted operator in the given differential equation.

The stability of the developed numerical method is established and its uniform convergence is proved. To validate the applicability of the method, one model problem is considered for numerical experimentation for different values of the perturbation parameter and mesh points.

In this paper, the authors consider a new governing problem having both small delay on convection term and large delay. As far as the researchers' knowledge is considered numerical solution of singularly perturbed boundary value problem containing both small delay and large delay is first being considered.