Delay-Dependent Stability for Recurrent Neural Networks With Time-Varying Delays

This brief is concerned with the stability for static neural networks with time-varying delays. Delay-independent conditions are proposed to ensure the asymptotic stability of the neural network. The delay-independent conditions are less conservative than existing ones. To further reduce the conservatism, delay-dependent conditions are also derived, which can be applied to fast time-varying delays. Expressed in linear matrix inequalities, both delay-independent and delay-dependent stability conditions can be checked using the recently developed algorithms. Examples are provided to illustrate the effectiveness and the reduced conservatism of the proposed result.      

Delay-Dependent Criteria for Global Robust Periodicity of Uncertain Switched Recurrent Neural Networks With Time-Varying Delay

In this paper, we introduce some ideas of switched systems into the field of neural networks and a large class of switched recurrent neural networks (SRNNs) with time-varying structured uncertainties and time-varying delay is investigated. Some delay-dependent robust periodicity criteria guaranteeing the existence, uniqueness, and global asymptotic stability of periodic solution for all admissible parametric uncertainties are devised by taking the relationship between the terms in the Leibniz-Newton formula into account. Because free weighting matrices are used to express this relationship and the appropriate ones are selected by means of linear matrix inequalities (LMIs), the criteria are less conservative than existing ones reported in the literature for delayed neural networks with parameter uncertainties. Some examples are given to show that the proposed criteria are effective and are an improvement over previous ones.     

New Approach to Delay-Dependent Stability Analysis and Stabilization for Continuous-Time Fuzzy Systems With Time-Varying Delay

This paper is concerned with delay-dependent stability analysis and stabilization problems for continuous-time Takagi and Sugeno (T-S) fuzzy systems with a time-varying delay. A new method for the delay-dependent stability analysis and stabilization is suggested, which is less conservative than other existing ones. First, based on a fuzzy Lyapunov-Krasovskii functional (LKF), a delay-dependent stability criterion is derived for the open-loop fuzzy systems. In the derivation process, some free fuzzy weighting matrices are introduced to express the relationships among the terms of the system equation, and among the terms in the Leibniz-Newton formula. Then, a delay-dependent stabilization condition based on the so-called parallel distributed compensation (PDC) scheme is worked out for the closed-loop fuzzy systems. The proposed stability criterion and stabilization condition are represented in terms of linear matrix inequalities (LMIs) and compared with the existing ones via two examples. Finally, application to control of a truck-trailer is also given to illustrate the effectiveness of the proposed design method.     

Delay-Dependent Criteria for Global Exponential Stability of Time-Varying Delayed Fuzzy Inertial Neural Networks

Neural Processing Letters - This paper is mainly concerned with global exponential stability of time-varying delayed fuzzy inertial neural networks. Different from previous approaches of variable...     

New Results on Stability of Discrete-Time Systems With Time-Varying State Delay

This note is concerned with the stability analysis of discrete-time systems with time-varying state delay. By defining new Lyapunov functions and by making use of novel techniques to achieve delay dependence, several new conditions are obtained for the asymptotic stability of these systems. The merit of the proposed conditions lies in their less conservativeness, which is achieved by circumventing the utilization of some bounding inequalities for cross products between two vectors and by paying careful attention to the subtle difference between the terms Sigma_m=k-dk ^k-1(middot) and Sigma _m=k-dM ^k-1(middot), which is largely ignored in the existing literature. These conditions are shown, via several examples, to be much less conservative than some existing result     

Delay Dependent Exponential Stability for Fuzzy Recurrent Neural Networks with Interval Time-Varying Delay

In this paper, the problem of delay-dependent exponential stability for fuzzy recurrent neural networks with interval time-varying delay is investigated. The delay interval has been decomposed into multiple non equidistant subintervals, on these interval Lyapunov-Krasovskii functionals (LKFs) are constructed to study stability analysis. Employing these LKFs, an exponential stability criterion is proposed in terms of Linear Matrix Inequalities (LMIs) which can be easily solved by MATLAB LMI toolbox. Numerical example is given to illustrate the effectiveness of the proposed method.     

Further Improvement on Delay-Dependent Global Robust Exponential Stability for Delayed Cellular Neural Networks with Time-Varying Delays

Neural Processing Letters - This paper is concerned with global robust exponential stability for a class of delayed cellular neural networks with time-varying delays. Some new sufficient conditions...     

Finite-Time Stability of Neural Networks with Impulse Effects and Time-Varying Delay

This paper introduces the design of the hyperconic multilayer perceptron (HC-MLP). Complex non-linear decision regions for classification purposes are generated by quadratic hyper-surfaces spawned by the hyperconic neurons in the hidden layer (for instance, spheres, ellipsoids, paraboloids, hyperboloids and degenerate conics). In order to generate quadratic hyper-surfaces, the hyperconic neurons’ transfer function includes the estimation of a quadratic polynomial. The proper assignment of decision regions to classes is achieved in the output layer by using spheres to determine whether a point is inside or outside the spherical region. The particle swarm optimization algorithm is used for training the HC-MLP. The learning of the HC-MLP selects the best conic surface that separates the data set vectors. For illustration purposes, two experiments are conducted using two distributions of synthetic data in order to show the advantages of HC-MLP when the patterns between classes are contiguous. Furthermore a comparison to the traditional multilayer perceptron is carried out to evaluate the complexity (in terms of the number of estimated patterns) and classification accuracy. HC-MLP is the principal component to implement a diagnosis system to detect faults in an induction motor and to implement an image segmentation system. The performance of HC-MLP is compared to other leading algorithms by using 4 databases commonly used in related literature.     

A Novel Delay-Dependent Criterion for Global Power Stability of Cellular Neural Networks with Proportional Delay

Neural Processing Letters - The global power stability of a class of cellular neural networks with proportional delay is considered in this paper. By proposing a new integral inequality and...     

Improved Delay-Dependent Asymptotic Stability Criteria for Delayed Neural Networks

This brief is concerned with asymptotic stability of neural networks with uncertain delays. Two types of uncertain delays are considered: one is constant while the other is time varying. The discretized Lyapunov–Krasovskii functional (LKF) method is integrated with the technique of introducing the free-weighting matrix between the terms of the Leibniz–Newton formula. The integrated method leads to the establishment of new delay-dependent sufficient conditions in form of linear matrix inequalities for asymptotic stability of delayed neural networks (DNNs). A numerical simulation study is conducted to demonstrate the obtained theoretical results, which shows their less conservatism than the existing stability criteria.      

New Results on Robust Exponential Stability of Uncertain Stochastic Neural Networks with Mixed Time-Varying Delays

This letter considers the robust exponential stability of uncertain stochastic neural networks with mixed time-varying delays. By using Lyapunov–Krasovskii functional and Itô’s differential formula, several new sufficient conditions guaranteeing the global robust exponential stability are derived in terms of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness and less conservativeness of our results.     

Finite-Time Stabilization for Static Neural Networks with Leakage Delay and Time-Varying Delay

Neural Processing Letters - The problem of finite-time stabilization (FTS) for static neural networks (SNNs) with leakage delay and time-varying delay is investigated in this paper. By introducing...     

Stability Analysis of Discrete-Time Recurrent Neural Networks With Stochastic Delay

This paper is concerned with the stability analysis of discrete-time recurrent neural networks (RNNs) with time delays as random variables drawn from some probability distribution. By introducing the variation probability of the time delay, a common delayed discrete-time RNN system is transformed into one with stochastic parameters. Improved conditions for the mean square stability of these systems are obtained by employing new Lyapunov functions and novel techniques are used to achieve delay dependence. The merit of the proposed conditions lies in its reduced conservatism, which is made possible by considering not only the range of the time delays, but also the variation probability distribution. A numerical example is provided to show the advantages of the proposed conditions.      

A Delay-Dependent Approach to Passivity Analysis for Uncertain Neural Networks with Time-varying Delay

This paper deals with the problem of passivity analysis for neural networks with time-varying delay, which is subject to norm-bounded time-varying parameter uncertainties. The activation functions are supposed to be bounded and globally Lipschitz continuous. Delay-dependent passivity condition is proposed by using the free-weighting matrix approach. These passivity conditions are obtained in terms of linear matrix inequalities, which can be investigated easily by using standard algorithms. Two illustrative examples are provided to demonstrate the effectiveness of the proposed criteria.     

Robust Stability of Switched Cohen–Grossberg Neural Networks With Mixed Time-Varying Delays

By combining Cohen-Grossberg neural networks with an arbitrary switching rule, the mathematical model of a class of switched Cohen-Grossberg neural networks with mixed time-varying delays is established. Moreover, robust stability for such switched Cohen-Grossberg neural networks is analyzed based on a Lyapunov approach and linear matrix inequality (LMI) technique. Simple sufficient conditions are given to guarantee the switched Cohen-Grossberg neural networks to be globally asymptotically stable for all admissible parametric uncertainties. The proposed LMI-based results are computationally efficient as they can be solved numerically using standard commercial software. An example is given to illustrate the usefulness of the results     

Stability Analysis of Takagi–Sugeno Fuzzy Cellular Neural Networks With Time-Varying Delays

This correspondence investigates the global exponential stability problem of Takagi-Sugeno fuzzy cellular neural networks with time-varying delays (TSFDCNNs). Based on the Lyapunov-Krasovskii functional theory and linear matrix inequality technique, a less conservative delay-dependent stability criterion is derived to guarantee the exponential stability of TSFDCNNs. By constructing a Lyapunov-Krasovskii functional, the supplementary requirement that the time derivative of time-varying delays must be smaller than one is released in the proposed delay-dependent stability criterion. Two illustrative examples are provided to verify the effectiveness of the proposed results     

Robust Stability Analysis for Interval Cohen–Grossberg Neural Networks With Unknown Time-Varying Delays

In this paper, robust stability problems for interval Cohen–Grossberg neural networks with unknown time-varying delays are investigated. Using linear matrix inequality, $M$ -matrix theory, and Halanay inequality techniques, new sufficient conditions independent of time-varying delays are derived to guarantee the uniqueness and the global robust stability of the equilibrium point of interval Cohen–Grossberg neural networks with time-varying delays. All these results have no restriction on the rate of change of the time-varying delays. Compared to some existing results, these new criteria are less conservative and are more convenient to check. Two numerical examples are used to show the effectiveness of the present results.      

Delay-Dependent Exponential Stability of Cellular Neural Networks with Multi-Proportional Delays

Global exponential stability of a class of cellular neural networks with multi-proportional delays is investigated. New delay-dependent sufficient conditions ensuring global exponential stability for the system presented here are related to the size of the proportional delay factor, by employing matrix theory and Lyapunov functional, and without assuming the differentiability, boundedness and monotonicity of the activation functions. Two examples and their simulation results are given to illustrate the effectiveness of the obtained results.     

An Improved Algebraic Criterion for Global Exponential Stability of Recurrent Neural Networks With Time-Varying Delays

This brief paper presents an M-matrix-based algebraic criterion for the global exponential stability of a class of recurrent neural networks with decreasing time-varying delays. The criterion improves some previous criteria based on M-matrix and is easy to be verified with the connection weights of the recurrent neural networks with decreasing time-varying delays. In addition, the rate of exponential convergence can be estimated via a simple computation based on the criterion herein.