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This paper is concerned with the problem of robust stability analysis for discrete-time neural networks with time-varying coupling delays, random parameter uncertainties and time-varying leakage delays. The uncertainties enter into the system parameters in a random way and such randomly occurring uncertainties obey certain mutually uncorrelated Bernoulli-distributed white noise sequences. The important feature of the results reported here is that the probability of occurrence of the parameter uncertainties are known a priori. Constructing suitable Lyapunov–Krasovskii functional (LKF) terms, sufficient conditions ensuring the stability of the discrete-time neural networks are derived in terms of linear matrix inequalities (LMIs). Finally, numerical examples are rendered to exemplify the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This paper investigates the finite-time boundedness (FTB) problem for a class of uncertain switched neural networks with time-varying delays. By exploring the mode-dependent properties of each subsystem, all the subsystems could be categorized into stable and unstable ones under the Lyapunov-like function framework. The sufficient conditions and a set of unified switching signals with average dwell time (ADT) are first derived with a known limit to the total activation time ratio between unstable and stable subsystems. Then, the obtained results are extended to a new switching approach with mode-dependent average dwell time (MDADT). Compared with general results, our proposed approach distinguishes the stable and unstable subsystems rather than viewing all subsystems as being unstable, thus getting less conservative switching criteria. Finally, a numerical example is provided to show the validity and the advantages of the finding techniques. [ABSTRACT FROM AUTHOR]

Abstract: This paper addresses the problem of robust filter design for a class of stochastic Markovian jump Hopfield neural networks with mode-dependent time-varying delays and norm-bounded parameter uncertainties. The purpose is to design a mode-dependent linear filtering which ensures that, for all admissible uncertainties, the filtering error system is not only stochastically asymptotically stable in the large, but also satisfies a prescribed level. Some novel mode-dependent and delay-dependent sufficient conditions for the solvability of this problem are obtained. The desired filter can be constructed by solving a set of strict linear matrix inequalities. A numerical example is provided to illustrate the effectiveness of the proposed method. [Copyright &y& Elsevier]

Abstract: This study is concerned with the problem of robust delay-probability-distribution-dependent stability of genetic regulatory networks with time-varying delays and parameter uncertainties. By dividing the time-varying delays into multiple nonuniformly subinterval and choosing an appropriate novel Lyapunov functional which contains some triple integral terms, new stability criteria are obtained and formulated in terms of linear matrix inequalities (LMIs). The uncertain parameters are modeled as having a structured linear fractional form. Besides, the derivatives of the time delays are considered having different bounds in various delay intervals. Moreover, less conservative conditions are obtained by using the lower bound lemma together with Jensen inequality lemma. Furthermore, the criteria can be applicable to both fast and slow time-varying delays. Finally, numerical examples are presented to illustrate the effectiveness of the theoretical results. [Copyright &y& Elsevier]

Abstract: This paper analyzes the robustness of global exponential stability of delayed recurrent neural networks (DRNNs) subject to parameter uncertainty in connection weight matrices. Given a globally exponentially stable DRNNs, the problem to be addressed herein is how much parameter uncertainty in the connection weight matrices that the neural network can remain to be globally exponentially stable. We characterize the upper bounds of the parameter uncertainty for the DRNNs to sustain global exponential stability. The upper bounds of parameter uncertainty intensity are characterized by using transcendental equations. Moreover, we prove theoretically that, for globally exponentially stable DRNNs, if additive parameter uncertainties in connection weight matrices are smaller than the derived supper bounds arrived at here, then the perturbed DRNNs are guaranteed to also be globally exponentially stable. A numerical example is provided to illustrate the theoretical results. [Copyright &y& Elsevier]

Abstract: This paper investigates robust and global exponential synchronizations in an array of nonidentical neural networks with leakage delays and impulsive coupling subject to parametric uncertainties. Some simpler sufficient conditions for synchronization are obtained when uncertainties vanish. A numerical example is given to illustrate the effectiveness of the theoretical results. [Copyright &y& Elsevier]

Abstract: Antilock braking system (ABS) is a highly nonlinear system including variation and uncertainties in the parameters due to changes in vehicle loadings, road condition, etc. It is a difficult task to design an ideal controller for ABS. In this paper, a novel robust controller named fractional order sliding mode controller (FOSMC) is proposed for ABS to regulate the slip to a desired value. The proposed FOSMC combines sliding mode controller (SMC) with fractional order dynamics, in which fractional order proportional-derivative (FOPD) sliding surface is adopted. FOSMC can not only deal with the uncertainties in ABS system but also track the desired slip faster than conventional integer order SMC with proportional or proportional-derivative sliding surface. Experimental results demonstrate the effectiveness of the proposed method. [Copyright &y& Elsevier]

Abstract: This paper analyzes the robustness of global exponential stability of recurrent neural networks subject to parameter uncertainty in connection weight matrix. Given a globally exponentially stable recurrent neural network, the problem to be addressed herein is how much parameter uncertainty in the connection weight matrix that the neural network can remain to be globally exponentially stable. We characterize the upper bounds of the parameter uncertainty for the recurrent neural networks to sustain global exponential stability. A numerical example is provided to illustrate the theoretical result. [Copyright &y& Elsevier]

Abstract: In the present paper, a new impulsive parabolic complex network (IPCN) with time-varying delays is proposed. Then, by constructing appropriate Lyapunov functionals and utilizing inequality techniques, some sufficient conditions are given to ensure that the proposed network model is globally exponentially stable. Furthermore, when the parameter uncertainties appear in the IPCN, several robust global exponential stability conditions are also presented. Finally, two examples with numerical simulations are provided to demonstrate the effectiveness of our criteria. [Copyright &y& Elsevier]

Abstract: In this paper, a robust adaptive fuzzy decentralized backstepping output feedback control approach is proposed for a class of uncertain large-scale stochastic nonlinear systems with unknown nonlinear functions, dynamical uncertainties and without the measurements of the states. The fuzzy logic systems are used to approximate the unknown nonlinear functions, and a fuzzy state observer is designed for estimating the unmeasured states. To solve the problem of the dynamical uncertainties, the changing supply function technique is incorporated into the backstepping recursive design technique, and a new robust adaptive fuzzy decentralized output feedback control approach is constructed. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) in probability, and the observer errors and the output of the system converge to a small neighborhood of the origin by choosing design parameters appropriately. A simulation example is provided to show the effectiveness of the proposed approach. [Copyright &y& Elsevier]

Abstract: In this paper, a robust parametric cerebellar model articulation controller (RP-CMAC) with self-generating design, called RPCSGD, is proposed for uncertain nonlinear systems. The proposed controller consists of two parts: one is the parametric CMAC with self-generating design (PCSGD), which is utilized to approximate the ideal controller and the other is the robust controller, which is designed to achieve a specified H ∞ robust tracking performance of the system. The corresponding memory size of the proposed controller can be suitably constructed via the self-generating design. Thus, the useless or untrained memories will not take possession of the space. Besides, the concept of sliding-mode control (SMC) is adopted so that the proposed controller has more robustness against the approximated error and uncertainties. The stability of the system can be guaranteed surely due to the derivations of the adaptive laws of the proposed RPCSGD based on the Lyapunov function. Finally, the proposed controller is applied to the second-order chaotic system and the one-link rigid robotic manipulator. The tracking performance and effectiveness of the proposed controller are verified by simulations of the computer. [Copyright &y& Elsevier]

Abstract: Artificial recurrent neural network has been proved to be a valuable tool in modeling nonlinear dynamical systems. Robustness study of recurrent neural network is critical to its successful implementation. The goal of robustness study is to reduce the sensitivity of modeling capability to parametric uncertainties or make the network fault tolerant. In this study, an uncertainty propagation analysis is performed to quantify the robustness of a recurrent neural network output due to perturbations in its trained weights. An uncertainty propagation analysis-based robustness measure has been proposed accordingly and further compared with available performance loss-based and sensitivity matrix-based approaches. Results show that the proposed robustness measure approach is more efficient, generic, and flexible to quantify the robustness of a recurrent neural network. [ABSTRACT FROM AUTHOR]

Abstract: A neural-network-based robust output feedback H ∞ control design is suggested for control of a class of nonlinear systems both with time delays and with uncertainties. In this paper, a full-order dynamic output feedback controller is designed for the delayed uncertain nonlinear system approximated by the neural network (e.g. multilayer perceptron, recurrent neural network, etc.), of which the activation functions satisfy the sector conditions. The closed-loop neural control system is transformed into a novel neural network model both with uncertainties and with time delays termed standard neural network model (SNNM). Based on the optimal robust H ∞ performance analysis of the SNNM, the parameters of output feedback controllers can be obtained by solving some linear matrix inequalities (LMIs). The optimal H ∞ controller ensures the robust global asymptotic stability of the closed-loop system and eliminates the effect of approximation errors, parametric uncertainties, and external disturbances. Finally, a simple example is presented to illustrate the effectiveness and the applicability of the proposed design approach. [Copyright &y& Elsevier]