Passivity analysis for discrete-time switched neural networks with various activation functions and mixed time delays

This paper is concerned with the passivity analysis for a class of discrete-time switched neural networks with various activation functions and mixed time delays. The mixed time delays under consideration include time-varying discrete delay and bounded distributed delay. By using the average dwell time approach and the discontinuous piecewise Lyapunov function technique, a novel delay-dependent sufficient condition for exponential stability of the switched neural networks with passivity is derived in terms of a set of linear matrix inequalities (LMIs). The obtained condition is not only dependent on the discrete delay bound, but also dependent on the distributed delay bound. A numerical example is given to demonstrate the effectiveness of the proposed result.     

Delay-independent stability criteria for complex-valued BAM neutral-type neural networks with time delays

This paper focuses on the global asymptotic stability of complex-valued bidirectional associative memory (BAM) neutral-type neural networks with time delays. By virtue of homeomorphism theory, inequality techniques and Lyapunov functional, a set of delay-independent sufficient conditions is established for assuring the existence, uniqueness and global asymptotic stability of an equilibrium point of the considered complex-valued BAM neutral-type neural network model. The assumption on boundedness of the activation functions is not required, and the LMI-based criteria are easy to be checked and executed in practice. Finally, we give one example with simulation to show the applicability and effectiveness of our main results.     

Quantized energy-to-peak state estimation for persistent dwell-time switched neural networks with packet dropouts

Nonlinear Dynamics - This paper pays close attention to the problem of energy-to-peak state estimation for a class of neural networks under switching mechanism. Persistent dwell-time switching...     

STABILITY ANALYSIS OF HOPFIELD NEURAL NETWORKS WITH TIME DELAY

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｒｅｃｅｎｔｙｅａｒｓｔｈｅｄｙｎａｍｉｃｂｅｈａｖｉｏｒｏｆｔｈｅｆｏｌｌｏｗｉｎｇＨｏｐｆｉｅｌｄｎｅｕｒａｌｎｅｔｗｏｒｋｓｍｏｄｅｌｗｉｔｈｔｉｍｅｄｅｌａｙｈａｖｅｂｅｅｎｉｎｖｅｓｔｉｇａｔｅｄｔｈｏｒｏｕｇｈｌｙＣｉ ｘｉ(ｔ) =-ｘｉＲｉ + ∑ｎｊ=1Ｔｉｊｆｊ(ｘｊ(ｔ-τｉｊ) ) +Ｉｉ　　 (ｉ=1 ,2 ,… ,ｎ) ,( 1 )ｗｈｅｒｅＲｉ,ＣｉａｎｄＩｉｒｅｐｒｅｓｅｎｔｒｅｓｉｓｔａｎｃｅ ,ｃａｐａｃｉｔａｎｃｅａｎｄｅｌｅｃｔｒｉｃｃｕｒｒｅｎｔ.Ｒｉ,Ｃｉａｒｅｐａ…     

Dissipativity analysis of stochastic neural networks with time delays

This paper is concerned with the dissipativity problem of stochastic neural networks with time delay. A new stochastic integral inequality is first proposed. By utilizing the delay partitioning technique combined with the stochastic integral inequalities, some sufficient conditions ensuring mean-square exponential stability and dissipativity are derived. Some special cases are also considered. All the given results in this paper are not only dependent upon the time delay, but also upon the number of delay partitions. Finally, some numerical examples are provided to illustrate the effectiveness and improvement of the proposed criteria.     

Global stability in switched recurrent neural networks with time-varying delay via nonlinear measure

In this paper, based on switched systems and recurrent neural networks (RNNs) with time-varying delay, the model of switched RNNs is formulated. Global asymptotical stability (GAS) and global robust stability (GRS) for such switched neural networks are studied by employing nonlinear measure and linear matrix inequality (LMI) techniques. Some new sufficient conditions are obtained to ensure GAS or GRS of the unique equilibrium of the proposed switched system. Furthermore, the proposed LMI results are computationally efficient as it can be solved numerically with standard commercial software. Finally, three examples are provided to illustrate the usefulness of the results.     

State estimation for Markovian jumping recurrent neural networks with interval time-varying delays

The paper is concerned with the state estimation problem for a class of neural networks with Markovian jumping parameters. The neural networks have a finite number of modes and the modes may jump from one to another according to a Markov chain. The main purpose is to estimate the neuron states, through available output measurements such that for all admissible time-delays, the dynamics of the estimation error are globally stable in the mean square. A new type of Markovian jumping matrix P _i is introduced in this paper. The discrete delay is assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Based on the new Lyapunov–Krasovskii functional, delay-interval dependent stability criteria are obtained in terms of linear matrix inequalities (LMIs). Finally, numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed LMI conditions.     

Adaptive exponential synchronization in pth moment for stochastic time varying multi-delayed complex networks

In this paper, the analysis problem of adaptive exponential synchronization in pth moment is considered for stochastic complex networks with time varying multi-delayed coupling. By using the Lyapunov–Krasovskii functional, stochastic analysis theory, several sufficient conditions to ensure the mode adaptive exponential synchronization in pth moment for stochastic delayed complex networks are derived. To illustrate the effectiveness of the synchronization conditions derived in this paper, a numerical example is finally provided.     

Nonlinear control for teleoperation systems with time varying delay

In this paper, we introduce delay-dependent control strategies for bilateral teleoperation systems in the presence of passive and constant input forces under time varying delay. We first design teleoperation systems where the local and remote sites are coupled by position signals of the master and slave manipulator. The design also combined undelayed position and velocity signals with nonlinear adaptive control terms to deal with the parametric uncertainties associated with the dynamical model of the master and slave manipulator. Then, we develop teleoperators by delaying position and velocity signals of the master and slave manipulator. Using Lyapunov–Krasovskii function, delay-dependent stability and tracking conditions for both teleoperators are developed in the presence of symmetrical and unsymmetrical time varying delays. The stability conditions are established in the presence of passive and constant human and environment interaction forces with the master and slave manipulators. Finally, simulation results are presented to demonstrate the validity of the theoretical development of the proposed designs for real-time teleoperation applications.     

Global exponential stability of stochastic memristor-based complex-valued neural networks with time delays

In recent years, the dynamic behaviors of complex-valued neural networks have been extensively investigated in a variety of areas. This paper focuses on the stability of stochastic memristor-based complex-valued neural networks with time delays. By using the Lyapunov stability theory, Halanay inequality and Itô formula, new sufficient conditions are obtained for ensuring the global exponential stability of the considered system. Moreover, the obtained results not only generalize the previously published corresponding results as special cases for our results, but also can be checked with the parameters of system itself. Finally, simulation results in three numerical examples are discussed to illustrate the theoretical results.     

A LMI-based approach to global asymptotic stability of neural networks with time varying delays

In this paper, the asymptotic stability of neural networks with time varying delay is studied by using the nonsmooth analysis, Lyapunov functional method and linear matrix inequality (LMI) technique. It is noted that the proposed results do not require smoothness of the behaved function and activation function as well as boundedness of the activation function. Several sufficient conditions are presented to show the uniqueness and the global asymptotical stability of the equilibrium point. Also, a high-dimensional matrix condition to ensure the uniqueness and the global asymptotical stability of equilibrium point can be reduced to a low-dimensional condition. The obtained results are easy to apply and improve some earlier works. Finally, we give two simulations to justify the theoretical analysis in this paper. This work was supported by the Natural Science Foundation of Jiangsu Province of China under Grant No. BK2006093.     

Reduced-order fault detection filter design for switched nonlinear systems with time delay

This paper investigates the problem of reduced-order robust fault detection filter (RFDF) design for a class of switched nonlinear systems with time-varying delay. The nonlinearities are assumed to satisfy global Lipschitz conditions. By using a generalized form of observer-based fault detection filter as a residual generator, the problem is formulated in the framework of H _∞ filtering. Based on the average dwell time approach and the Lyapunov functional technique, a sufficient delay-dependent criterion on the existence of the RFDF is derived to ensure the exponential stability and a prescribed L ₂-gain bound of the residual error system. Furthermore, the parameters of an admissible filter are obtained from the solution of a convex optimization problem. A practical example is provided to illustrate the effectiveness of the proposed results.     

Exponential synchronization of stochastic delayed discrete-time complex networks

This paper is concerned with the problem of synchronization for stochastic discrete-time drive-response networks with time-varying delay. By employing the Lyapunov functional method combined with the stochastic analysis as well as the feedback control technique, several sufficient conditions are established that guarantee the exponentially mean-square synchronization of two identical delayed networks with stochastic disturbances. These sufficient conditions, which are expressed in terms of linear matrix inequalities (LMIs), can be solved efficiently by the LMI toolbox in Matlab. A particular feature of the LMI-based synchronization criteria is that they are dependent not only on the connection matrices in the drive networks and the feedback gains in the response networks, but also on the lower and upper bounds of the time-varying delay, and are therefore less conservative than the delay-independent ones. Two numerical examples are exploited to demonstrate the feasibility and applicability of the proposed synchronization approaches.     

Robust state estimation for discrete-time genetic regulatory networks with randomly occurring uncertainties

In this paper, we investigate the problem of robust state estimator design for a class of uncertain discrete-time genetic regulatory networks (GRNs) with time varying delays and randomly occurring uncertainties. By introducing a new discretized Lyapunov–Krasovskii functional together with a free-weighting matrix technique, first we derive a set of sufficient conditions for the existence of global asymptotic state estimator for the discrete-time GRN model with time delays satisfying both the lower and the upper bound of the interval time-varying delay. Further, the obtained results are extended to deal the robust state estimator design for the discrete-time GRN model in the presence of randomly occurring uncertainties which obey certain mutually uncorrelated Bernoulli distributed white noise sequences. The proposed criterions are established in terms of linear matrix inequalities (LMIs) which can be easily solved via Matlab LMI toolbox. Finally, the robust state estimator design has been implemented in a gene network model to illustrate the applicability and usefulness of the obtained theory.     

Robust observer for discrete-time Markovian jumping neural networks with mixed mode-dependent delays

The robust observer problem is considered in this paper for a class of discrete-time neural networks with Markovian jumping parameters and mode-dependent time delays which are in both discrete-time form and finite distributed form. The neural network switches from one mode to another controlled by a Markov chain with known transition probability. Time-delays considered in this paper are mode-dependent which may reflect a more realistic version of the neural network. By using the Lyapunov functional method and the techniques of linear matrix inequalities (LMIs), sufficient conditions are established in terms of LMIs that ensure the existence of the robust observer. The obtained conditions are easy to be verified via the LMI toolbox. An example is presented to show the effectiveness of the obtained results.     

Non-fragile extended dissipative state estimation for delayed discrete-time neural networks: application to quadruple tank process model

Nonlinear Dynamics - This paper deals with the non-fragile state estimator design to study the robust extended dissipativity criterion for a class of discrete-time neural networks (DNNs) involving...     

Super-twisting algorithm with time delay estimation for uncertain robot manipulators

Nonlinear Dynamics - In a small tubular neighborhood of the heteroclinic orbits, we establish a local coordinate system by using the foundational solutions of the linear variational equation of the...