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This paper sets out to describe transform methods to control vendor‐managed inventory (VMI). It aims to examine the limits of modelling approaches within control‐theoretic models.

Modelling was achieved with the Simulink package using the equations developed by Disney and Towill for a two‐tier VMI system. Discrete and continuous models were considered together with two forms of production delays: a finite delay and the Forrester exponential delay. Standard control engineering analyses of these delay representations were compared to illustrate how the system response and stability depend on their formulation and to determine the permissible gains.

Response by a discrete or continuous model to step inputs in sales rates depends on the type of delay representation but the responses do not differ by more than 5 per cent if the same delay form is used in the models. The prime effect of using a finite delay is to deepen the stock‐out and increase the required order rate compared with the same response observed with the use of exponential forms of delay. Total time for recovery is similar with all models. It is shown that the continuous model with an exponential delay is always stable and when using a fixed delay the continuous model can be made stable.

The models presented here illustrate that the various forms of control‐theoretic models present similar results irrespective of technique used, provided that they have the same delay type. The range of gains for the required order rate can be computed for any VMI system, knowing that they can be designed to guarantee stable operation.

This work extends that of Disney and Towill to include different modelling representations. It allows operational gains to be safely chosen for stable operation.

The purpose of this paper is to study the dynamic behavior of complex-valued switched grey neural network models (SGNMs) with distributed delays when the system parameters and external input are grey numbers.

Firstly, by using the properties of grey matrix, M-matrix theory and Homeomorphic mapping, the existence and uniqueness of equilibrium point of the SGNMs were discussed. Secondly, by constructing a proper Lyapunov functional and using the average dwell time approach and inequality technique, the robust exponential stability of the SGNMs under restricted switching was studied. Finally, a numerical example is given to verify the effectiveness of the proposed results.

Sufficient conditions for the existence and uniqueness of equilibrium point of the SGNMs have been established; sufficient conditions for guaranteeing the robust stability of the SGNMs under restricted switching have been obtained.

(1) Different from asymptotic stability, the exponential stability of SGNMs which include grey parameters and distributed time delays will be investigated in this paper, and the exponential convergence rate of the SGNMs can also be obtained; (2) the activation functions, self-feedback coefficients and interconnected matrices are with different forms in different subnetworks; and (3) the results obtained by LMIs approach are complicated, while the proposed sufficient conditions are straightforward, which are conducive to practical applications.

The purpose of this paper is to investigate the existence and global exponential stability of periodic solution of memristor-based recurrent neural networks with time-varying delays and leakage delays.

The differential inequality theory and some novel mathematical analysis techniques are applied.

A set of sufficient conditions which guarantee the existence and global exponential stability of periodic solution of involved model is derived.

It plays an important role in designing the neural networks.

The obtained results of this paper are new and complement some previous studies. The innovation of this paper concludes two aspects: the analysis on the existence and global exponential stability of periodic solution of memristor-based recurrent neural networks with time-varying delays and leakage delays is first proposed; and it is first time to establish the sufficient criterion which ensures the existence and global exponential stability of periodic solution of memristor-based recurrent neural networks with time-varying delays and leakage delays.

Trajectory tracking is an important issue to underactuated unmanned surface vehicles (USVs). However, parametric uncertainties and environmental disturbances bring great challenges to the precise trajectory tracking control of USVs. This paper aims to propose a robust trajectory tracking control algorithm with exponential stability for underactuated USVs with parametric uncertainties and unknown environmental disturbances.

In this method, the backstepping method and sliding mode control method are combined to ensure that the underactuated USV can track and maintain the desired trajectory. In addition, a modified switching-gain adaptation algorithm is adopted to enhance the robustness and reduce chattering. Besides, the global exponential stability of the closed-loop system is proved by Lyapunov’s direct method.

The proposed method in this paper offers a robust trajectory tracking solution to underactuated USVs and it is verified by simulations and experiments. Compared with the traditional proportion-integral-derivative method and several state-of-the-art algorithms, the proposed method has superior performance in simulation and experimental results.

This paper proposes a robust trajectory tracking control algorithm with exponential stability for underactuated USVs. The proposed method achieves exponential stability with better robustness and transient performance.

The purpose of this paper is to obtain the criteria of p‐moment exponential robust stability for a class of grey neutral stochastic delay systems.

By constructing a Lyapunov‐Krasovskii functional and employing the decomposition technique of continuous matrix‐covered sets of grey matrix and using three key inequalities, the paper investigates the p‐moment exponential robust stability for a class of grey neutral stochastic delay systems. A numeric example is given to demonstrate the effectiveness of the criteria presented in the paper.

The results not only can be used to judge the p‐moment exponential robust stability of the systems researched in the paper, but also can be applied in the stability analysis of grey non‐neutral stochastic systems.

The method exposed in the paper can be used in the analysis and designation of practical stochastic control systems.

The paper succeeds in obtaining the criteria of p‐moment exponential robust stability for grey neutral stochastic delay systems by constructing a Lyapunov‐Krasovskii functional and employing the decomposition technique of continuous matrix‐covered sets of grey matrix and using three key inequalities.

The purpose of this paper is to develop a methodology for the existence and global exponential stability of the unique equilibrium point of a class of impulsive Cohen‐Grossberg neural networks.

The authors perform M‐matrix theory and homeomorphism mapping principle to investigate a class of impulsive Cohen‐Grossberg networks with time‐varying delays and distributed delays. The approach builds on new sufficient criterion without strict conditions imposed on self‐regulation functions.

The authors' approach results in new sufficient criteria easy to verify but without the usual assumption that the activation functions are bounded and the time‐varying delays are differentiable. An example shows the effectiveness and superiority of the obtained results over some previously known results.

The novelty of the proposed approach lies in removing the usual assumption that the activation functions are bounded and the time‐varying delays are differentiable, and the use of M‐matrix theory and homeomorphism mapping principle for the existence and global exponential stability of the unique equilibrium point of a class of impulsive Cohen‐Grossberg neural networks.

This paper deals with the problem of input/output-to-state stability (IOSS) of direct-form digital filters, which simultaneously contain external disturbances and two's complement nonlinearity. The nonlinearity under consideration is confined to the sector [–1, 1], which contains saturation, zeroing, two's complement and triangular.

The proposed condition is based on IOSS approach, which is capable of providing a framework for checking and analysing the stability of nonlinear system based on input as well as output information.

A linear matrix inequality (LMI)-based new sufficient criterion for the IOSS of the suggested system is obtained. The obtained criterion is capable of detecting the output-to-state stability (OSS) and asymptotic stability of direct-form digital filters with zero external disturbances. In addition, state-norm estimator for the filter under consideration is constructed by adopting an exponential-decay IOSS criterion. Several examples are provided to illustrate the usefulness of the proposed criteria.

The result of the paper is introduced for the first time, and it is suitable for stability analysis of interfered direct-form digital filter with two's complement overflow using IOSS approach.

The purpose of this paper is to develop a new criterion for the exponential stability and

_∞ performance of state-space digital filters under the influence of any combination of quantization/overflow nonlinearities.

The proposed criterion uses the

_∞ approach that is suitable for the design of discrete system in the presence of external disturbance. Analysis and synthesis in an

_∞ setting is advantageous as it proposes effective disturbance attenuation, less sensitivity to uncertainties and many practical applications.

The criterion not only guarantees exponential stability but also reduces the effect of external interference. A numerical example demonstrating the effectiveness of the proposed method is given.

The main result of the paper is reported for the first time and it is useful to ensure the stability of digital filters in the presence of external disturbance and any combination of quantization/overflow nonlinearities.

The purpose of this paper is to report on the global practical uniform h-stabilization for certain classes of nonlinear time-varying systems and its application in a separately excited DC motor circuit.

Based on Lyapunov theory, the practical h-stabilization result is derived to guarantee practical h-stability and applicated in a separately excited DC motor.

A controller is designed and added to the nonlinear time-varying system. The practical h-stability of the nonlinear control systems is guaranteed by applying the appropriate controller based on Lyapunov second method. Another effective controller is also designed for the global practical uniform h-stability on the separately excited DC motor with load. Numerical simulations are demonstrated to verify the effectiveness of the proposed controller scheme.

The introduced approach is interesting for practical h-stabilization of nonlinear time-varying systems and its application in a separately excited DC motor. The original results generalize well-known fundamental result: practical exponential stabilization for nonlinear time-varying systems.

The purpose of this paper is to investigate the weighted pseudo-almost periodic solutions of shunting inhibitory cellular neural networks (SICNNs) with time-varying delays and distributed delays.

The principle of weighted pseudo-almost periodic functions and some new mathematical analysis skills are applied.

A set of sufficient criteria which guarantee the existence and exponential stability of the weighted pseudo-almost periodic solutions of the considered SICNNs are established.

The derived results of this paper are new and complement some earlier works. The innovation of this paper concludes two points: a new sufficient criteria guaranteeing the existence and exponential stability of the weighted pseudo-almost periodic solutions of SICNNs are established; and the ideas of this paper can be applied to investigate some other similar neural networks.