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As a class of stochastic hybrid systems, Markovian jump systems have been extensively studied in the past decades. In light of some results obtained on this topic. The purpose of this paper is to investigate the stability problems for delayed Markovian jump systems.

The time‐varying‐delays considered in this paper are switched synchronously with system mode. Based on stochastic Lyapunov theory, the delay‐dependent stability conditions are developed by using some linear matrix inequality techniques. To obtain better stability criteria, the different Lyapunov‐Krasovskii functional is chosen and an important inequality is introduced.

Numerical examples show that the resulting criteria in this paper have advantages over some previous ones in that they involve fewer matrix variables, but have less conservatism. Furthermore, they only involve the matrix variables appeared in the Lyapunov functional. Therefore, there are no additional matrix variables coupled with the system matrices, which will be easier to investigate the synthesis problems for the underlying systems and save much computation.

The introduced approach is more efficient to investigate the stability for Markovian jump systems with mode‐dependent time‐varying‐delays.

For most practical control system problems, the state variables of a system are not often available or measureable due to technical or economical constraints. In these cases, an observer-based controller design problem, which is involved with using the available information on inputs and outputs to reconstruct the unmeasured states, is desirable, and it has been wide investigated in many practical applications. However, the investigation on a discrete-time singular Markovian jumping system is few so far. This paper aims to consider an observer-based control problem for a discrete-time singular Markovian jumping system and provides a set of easy-used conditions to the proposed control law.

According to the connotation of the separation principle extended from linear systems, a mode-dependent observer and a state-feedback controller is designed and carried out independently via two sets of derived necessary and sufficient conditions in terms of linear matrix inequalities (LMIs).

A set of necessary and sufficient conditions for an admissibility analysis problem related to a discrete-time singular Markovian jumping system is derived to be a doctrinal foundation for the proposed design problems. A mode-dependent observer and a controller for such systems could be designed via two sets of strictly LMI-based synthesis conditions.

The proposed method can be applied to discrete-time singular Markovian jumping systems with transition probability p_ij > 0 rather than the ones with p_ii = 0.

The formulated problem and proposed methods have extensive applications in various fields such as power systems, electrical circuits, robot systems, chemical systems, networked control systems and interconnected large-scale systems. Take robotic networked control systems for example. It is recognized that the variance phenomena derived from network transmission, such as packets dropout, loss and disorder, are suitable for modeling as a system with Markovian jumping modes, while the dynamics of the robot systems can be described by singular systems. In addition, the packets dropout or loss might result in unreliable transmission signals which motivates an observer-based control problem.

Both of the resultant conditions of analysis and synthesis problems for a discrete-time singular Markovian jumping system are necessary and sufficient, and are formed in strict LMIs, which can be used and implemented easily via MATLAB toolbox.

The purpose of this paper is to develop a methodology for the stochastically asymptotic synchronization problem for a class of neutral-type chaotic neural networks with both leakage delay and Markovian jumping parameters under impulsive perturbations.

The authors perform drive-response concept and time-delay feedback control techniques to investigate a class of neutral-type chaotic neural networks with both leakage delay and Markovian jumping parameters under impulsive perturbations. New sufficient criterion is established without strict conditions imposed on the activation functions.

It turns out that the approach results in new sufficient criterion easy to be verified but without the usual assumption of the differentiability and monotonicity of the activation functions. Two examples show the effectiveness of the obtained results.

The novelty of the proposed approach lies in removing the usual assumption of the differentiability and monotonicity of the activation functions, and the use of the Lyapunov functional method, Jensen integral inequality, a novel Gu’s lemma, reciprocal convex and linear convex combination technique for the stochastically asymptotic synchronization problem for a class of neutral-type chaotic neural networks with both leakage delay and Markovian jumping parameters under impulsive perturbations.

The purpose of this paper is to develop a methodology for the stochastically asymptotic stability of fuzzy Markovian jumping neural networks with time-varying delay and continuously distributed delay in mean square.

The authors perform Briat Lemma, multiple integral approach and linear convex combination technique to investigate a class of fuzzy Markovian jumping neural networks with time-varying delay and continuously distributed delay. New sufficient criterion is established by linear matrix inequalities conditions.

It turns out that the obtained methods are easy to be verified and result in less conservative conditions than the existing literature. Two examples show the effectiveness of the proposed results.

The novelty of the proposed approach lies in establishing a new Wirtinger-based integral inequality and the use of the Lyapunov functional method, Briat Lemma, multiple integral approach and linear convex combination technique for stochastically asymptotic stability of fuzzy Markovian jumping neural networks with time-varying delay and continuously distributed delay in mean square.

This paper aims to study the attitude control problem with mutating orbital rate and actuator fading.

To avoid malicious physical attacks and hide itself, the spacecraft may irregularly switch its orbit altitude within a specific range, which will bring about variations in orbital rate, thereby causing mutations in the attitude dynamics model. The actuator faults will also cause changes in system dynamics. Both factors affect the control performance. First, this paper determines the potential switching orbits. Then under different conditions, design controllers that can accommodate actuator faults according to the statistical law of actuator fading.

This paper, to the best of the authors’ knowledge, for the first time, introduces the Markovian jump framework to model the possible unexpected mutating of orbital rate and actuator fading of spacecraft and then designs a novel control policy to solve the attitude control problem.

This paper also provides the algorithm design processes in detail. A comparative numerical simulation is given to verify the effectiveness of the proposed algorithm.

This is an early solution for spacecraft attitude control with dynamics model mutations.

This paper aims to study the issues of output reachable set estimation for the linear singular Markovian jump systems (SMJSs) with time-varying delay based on a proportional plus derivative (PD) bumpless transfer (BT) output feedback (OF) control scheme.

To begin with, a sufficient criterion is given in the form of a linear matrix inequality based on the Lyapunov stability theory. Then, a PD-BT OF controller is designed to keep all the output signs of the system are maintain within a predetermined ellipsoid. Finally, numerical and practical examples are used to demonstrate the efficiency of the approach.

Based on PD control and BT control method, an OF control strategy for the linear SMJSs with time-varying delay is proposed.

The output reachable set synthesis of linear SMJSs with time-varying delay can be solved by using the proposed approach. Besides, to obtain more general results, the restrictive assumptions of some parameters are removed. Furthermore, a sufficiently small ellipsoid can be obtained by the design scheme adopted in this paper, which reduces the conservatism of the existing results.

To control one of the joints during the actual movement of the hydraulically driven quadruped robot, all the other joints in the leg need to be locked. Once the joints are unlocked, there is a coupling effect among the joints. Therefore, during the normal exercise of the robot, the movement of each joint is affected by the coupling of other joints. This brings great difficulties to the coordinated motion control of the multi-joints of the robot. Therefore, it is necessary to reduce the influence of the coupling of the hydraulically driven quadruped robot.

To solve the coupling problem with the joints of the hydraulic quadruped robot, based on the principle of mechanism dynamics and hydraulic control, the dynamic mathematical model of the single leg mechanism of the hydraulic quadruped robot is established. On this basis, the coupling dynamics model of the two joints of the thigh and the calf is derived. On the basis of the multivariable decoupling theory, a neural network (NN) model reference decoupling controller is designed.

The simulation and prototype experiment are carried out between the thigh joint and the calf joint of the hydraulic quadruped robot, and the results show that the proposed NN model reference decoupling control method is effective, and this method can reduce the cross-coupling between the thigh and the calf and improve the dynamic characteristics of the single joint of the leg.

The proposed method provides technical support for the mechanical–hydraulic cross-coupling among the joints of the hydraulic quadruped robot, achieving coordinated movement of multiple joints of the robot and promoting the performance and automation level of the hydraulic quadruped robot.

On the basis of the theory of multivariable decoupling, a new decoupling control method is proposed, in which the mechanical–hydraulic coupling is taken as the coupling behavior of the hydraulic foot robot. The method reduces the influence of coupling of system, improves the control precision, realizes the coordinated movement among multiple joints and promotes the popularization and use of the hydraulically driven quadruped robot.

The purpose of this paper is to find two iterative methods to solve the general coupled matrix equations over the generalized centro‐symmetric and central antisymmetric matrices.

By extending the idea of conjugate gradient (CG) method, the authors present two iterative methods to solve the general coupled matrix equations over the generalized centro‐symmetric and central antisymmetric matrices.

When the general coupled matrix equations are consistent over the generalized centro‐symmetric and central anti‐symmetric matrices, the generalized centro‐symmetric and central anti‐symmetric solutions can be obtained within nite iterative steps. Also the least Frobenius norm generalized centrosymmetric and central anti‐symmetric solutions can be derived by choosing a special kind of initial matrices. Furthermore, the optimal approximation generalized centrosymmetric and central anti‐symmetric solutions to given generalized centro‐symmetric and central anti‐symmetric matrices can be obtained by finding the least Frobenius norm generalized centro‐symmetric and central anti‐symmetric solutions of new matrix equations. The authors employ some numerical examples to support the theoretical results of this paper. Finally, the application of the presented methods is highlighted for solving the projected generalized continuous‐time algebraic Lyapunov equations (GCALE).

By the algorithms, the solvability of the general coupled matrix equations over generalized centro‐symmetric and central anti‐symmetric matrices can be determined automatically. The convergence results of the iterative algorithms are also proposed. Several examples and an application are given to show the efficiency of the presented methods.

The purpose of this paper is to develop a method for the existence, uniqueness and globally robust stability of the equilibrium point for Cohen–Grossberg neural networks with time-varying delays, continuous distributed delays and a kind of discontinuous activation functions.

Based on the Leray–Schauder alternative theorem and chain rule, by using a novel integral inequality dealing with monotone non-decreasing function, the authors obtain a delay-dependent sufficient condition with less conservativeness for robust stability of considered neural networks.

It turns out that the authors’ delay-dependent sufficient condition can be formed in terms of linear matrix inequalities conditions. Two examples show the effectiveness of the obtained results.

The novelty of the proposed approach lies in dealing with a new kind of discontinuous activation functions by using the Leray–Schauder alternative theorem, chain rule and a novel integral inequality on monotone non-decreasing function.

The operational aspects of supply chain, when handled correctly, results in diminishing the impact of the bullwhip effect. The purpose of this study is to analyze the impact of operational and financial variables on the bullwhip effect. Various operational factors that contribute to the bullwhip effect in a supply chain are identified and their impact on variability in production is measured at manufacturer’s end in the supply chain.

Ten different sectors of the Indian economy are identified and analyzed on the basis of bullwhip effect. The ratio of change in production with respect to change in demand is taken as a metric to measure the bullwhip effect. Initially, the impact of identified variables on bullwhip effect is analyzed using the linear regression analysis and then to gain more insights, the threshold regression model is applied according to the change in bullwhip ratio.

The study identifies four threshold regions in which bullwhip ratio is changing its slope considerably. The operational and financial variables impacting bullwhip effect differently in these four regions provide useful insights about how the variables are impacting the bullwhip effect.

Past 11 years of observations on identified operational and financial variables are studied for ten different sectors. The operational and financial variables are identified on basis of available literature but may not be exhaustive in nature.

The present study implies that the emphasis must be given to the magnitude of the bullwhip ratio. Strategies must be adopted that result in mitigation of bullwhip effect. Such mitigation strategies must not only be restricted on the basis of type of product or sector, perhaps they must be on the basis of threshold region of bullwhip ratio.

The study suggests a novel approach to study the bullwhip effect in supply chain management using the application of threshold regression considering the bullwhip ratio as a threshold variable.