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In this study, a robust adaptive control is proposed for a class of strict-feedback state delayed non-linear systems with unmodelled dynamics and distributed time-varying delays using radial basis function neural networks. Dynamic uncertainties are dealt with using separation technique and introducing a dynamic signal. The terms including state time-varying delay and distributed time-varying delay uncertainties are compensated for by constructing appropriate Lyapunov–Krasovskii functionals. Using Young's inequality, only one learning parameter need to be tuned online at each step of recursion. It is proved that the proposed design method is able to guarantee semi-global uniform ultimate boundedness of all signals in the closed-loop system. Simulation results demonstrate the effectiveness of the proposed approach.

In this article, we study the problem of robust H∞ performance analysis for a class of uncertain Markovian jump systems with mixed overlapping delays. Our aim is to present a new delay‐dependent approach such that the resulting closed‐loop system is stochastically stable and satisfies a prescribed H∞ performance level χ. The jumping parameters are modeled as a continuous‐time, finite‐state Markov chain. By constructing new Lyapunov‐Krasovskii functionals, some novel sufficient conditions are derived to guarantee the stochastic stability of the equilibrium point in the mean‐square. Numerical examples show that the obtained results in this article is less conservative and more effective. The results are also compared with the existing results to show its conservativeness. © 2016 Wiley Periodicals, Inc. Complexity 21: 460–477, 2016

This article investigates the stability analysis of discrete‐time neural networks with time‐varying delays by the utilization of quadratic delay information. First, three extended negative‐definiteness lemmas for matrix‐valued quadratic function with different matrices injection are established. Second, a novel delay‐product‐type Lyapunov functional with the asymmetric summation is developed to relax the positive‐definiteness of functional. Then, the proposed negative definite approaches are utilized in combination with some typical summation inequalities to realize the construction of linear matrix inequalities. Based on these improved technologies, two delay‐dependent stability criteria with less conservatism and fewer computational burdens are derived. Finally, several numerical examples are presented to show the validity and superiority of the proposed methods. This article investigates the stability analysis of discrete‐time neural networks with time‐varying delays by the utilization of quadratic delay information. First, three extended negative‐definiteness lemmas for matrix‐valued quadratic function with different matrices injection are established. Second, a novel delay‐product‐type Lyapunov functional with the asymmetric summation is developed to relax the positive‐definiteness of functional. Then, the proposed negative definite approaches are utilized in combination with some typical summation inequalities to realize the construction of linear matrix inequalities. Based on these improved technologies, two delay‐dependent stability criteria with less conservatism and fewer computational burden are derived. Finally, several numerical examples are presented to show the validity and superiority of the proposed methods.

In this study, a novel method based on a robust adaptive fuzzy control approach is developed for nonlinear teleoperation systems. Its main objectives are to ensure system stability and properly mitigating parametric uncertainties stemming from external disturbances and un‐modelled dynamics. For the communication channel, instead of the direct transmission of environmental torque signals, the approximated environmental parameters by the fuzzy system are transmitted to the master side for the prediction of environmental torque, thus successfully avoiding the transmission of the power signals in the delayed communication channel and solving the passivity problem in the teleoperation system. Besides, a trajectory generator is employed in the master side, whereas a trajectory smoothing is provided in the slave side. Theoretically, it was proven that both position tracking and force feedback problems are attained. Using Lyapunov stability analysis, this work illustrates that the robust adaptive fuzzy controller based on the backstepping approach guarantees the system's asymptotic stability. Simulation results confirm the efficiency of the suggested control technique in achieving the stability and tracking objectives of the uncertain nonlinear teleoperation system. In this study, a novel backstepping‐based method based on a robust adaptive fuzzy control approach for nonlinear teleoperation systems has been developed to overcome the parametric uncertainties (including external disturbances and un‐modelled dynamics). For the communication channel, instead of the direct transmission of environmental torque signals, the fuzzy approximate environmental parameters are transmitted to the master side for prediction of environmental torque, which successfully avoids the transmission of the power signals in the delayed communication channel and it solves the passivity problem in the teleoperation system.

This paper proposes a new distributed fault estimation method based on the L1 $\\mathcal {L}_1$performance, along with its circuit implementation. In order to achieve this objective, the paper begins by offering a thorough model of interconnected systems with time‐varying delays, which incorporates multiple faults, input/output disturbances, and uncertainties. Next, a set of L1 $\\mathcal {L}_1$distributed estimators is designed to simultaneously estimate the states of the system as well as different types of faults including actuator and sensor faults within all subsystems. This observer is robust against disturbances, uncertainties, and time‐varying communication delays. To this end, sufficient conditions are formulated as linear matrix inequalities to ensure that the dynamics related to estimation errors remain robustly stable and also attenuate disturbances. The estimation accuracy and robustness of the proposed approach are studied by an illustrative example. Furthermore, its effectiveness and superior performance are confirmed by comparison with the related methods in the literature. Additionally, the circuit implementations of the system and the suggested estimator are presented for practical applications. This paper proposes a new distributed fault estimation method for interconnected systems with time varying delays and subject to multiple faults, input/output disturbances, and uncertainties. The distributed estimator is designed to simultaneously estimate the states of the system as well as different types of faults including actuator and sensor faults within all subsystems. Sufficient conditions of stability of the estimation dynamic are obtained as linear matrix inequalities.

This article is concerned with the problem of pinning outer synchronization between two complex delayed dynamical networks via adaptive intermittent control. At first, a general model of hybrid‐coupled dynamical network with time‐varying internal delay and time‐varying coupling delay is given. Then, an aperiodically adaptive intermittent pinning‐control strategy is introduced to drive two such delayed dynamical networks to achieve outer synchronization. Some sufficient conditions to guarantee global outer‐synchronization are derived by constructing a novel piecewise Lyapunov function and utilizing stability analytical method. Moreover, a simple pinned‐node selection scheme determining what kinds of nodes should be pinned first is provided. It is noted that the adaptive pinning control type is aperiodically intermittent, where both control period and control width are non‐fixed. Finally, a numerical example is given to illustrate the validity of the theoretical results. © 2016 Wiley Periodicals, Inc. Complexity 21: 593–605, 2016

This paper considers the impulsive control of unstable neural networks with unbounded timevarying delays, where the time delays to be addressed include the unbounded discrete time-varying delay and unbounded distributed time-varying delay. By employing impulsive control theory and some analysis techniques, several sufficient conditions ensuring μ-stability, including uniform stability,（global） asymptotical stability, and（global） exponential stability, are derived. It is shown that an unstable delay neural network,especially for the case of unbounded time-varying delays, can be stabilized and has μ-stability via proper impulsive control strategies. Three numerical examples and their simulations are presented to demonstrate the effectiveness of the control strategy.

This article studies the observer‐based integral sliding mode control (ISMC) problem for continuously uncertain neutral semi‐Markovian jumping systems with time‐varying delays (TDs). Firstly, based on the designed state observer, an ISMC method is proposed for the first time. Then, building an appropriate stochastic Lyapunov–Krasovskii functional by taking into account more information about TDs, a novel sufficient condition is established for the robustly stochastic stability of the overall system made up of the error system and the sliding mode dynamics system. Furthermore, an ISMC law is devised to ensure the reachability of the integral sliding surface in a finite time. Additionally, the proposed method can be reduced to the known state case, thus, the ISMC problem for continuously uncertain neutral semi‐Markovian jumping systems with TDs is also investigated in this article. Finally, three numerical examples explain the effectiveness of the results obtained. This article studies the observer‐based integral sliding mode control (ISMC) problem for continuously uncertain neutral semi‐Markovian jumping systems with time‐varying delays. Firstly, based on the designed state observer propose an ISMC method. Then, through Lyapunov–Krasovskii functional method establish a novel sufficient condition. Finally, an ISMC law is devised to ensure the reachability of the sliding surface in a finite time.

This paper reports a designed method of fault diagnosis, estimation, and fault-tolerant control aiming at solving the problems of time–delay variation of system parameters, actuator time-varying failure, and external disturbance under the flight mode of air-ground platform. Firstly, a robust fault observer is designed to accurately detect the fault of unmanned air-ground attitude system with time-varying parameter delay and reduce the false alarm rate through reasonable assumptions; secondly, considering the actual computing power of the system, the method of estimating the overall fault size of the system instead of estimating each sub fault separately is adopted to reduce the memory space and computation. Then, based on the fault diagnosis and estimation, the fault-tolerant control rate is designed, the integral term is reasonably introduced to eliminate the chattering problem in the fault-tolerant control, and the appropriate nonlinear function is selected as the ideal control input to optimize the transient performance of the system. Finally, the stability of the system is proved, and the effectiveness of the proposed method is verified by simulation.

This article deals with the state estimation problem of memristor‐based recurrent neural networks (MRNNs) with time‐varying delay based on passivity theory. The main purpose is to estimate the neuron states, through available output measurements such that for all admissible time delay, the dynamics of the estimation error is passive from the control input to the output error. Based on the Lyapunov–Krasovskii functional (LKF) involving proper triple integral terms, convex combination technique, and reciprocal convex technique, a delay‐dependent state estimation of MRNNs with time‐varying delay is established in terms of linear matrix inequalities (LMIs). The information about the neuron activation functions and lower bound of the time‐varying delays is fully used in the LKF. Then, the desired estimator gain matrix is accomplished by solving LMIs. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed theoretical results. © 2013 Wiley Periodicals, Inc. Complexity 19: 32–43, 2014