Exponential State Estimation for Neural Networks with Leakage, Discrete and Distributed Delays

In this paper, the design problem of state estimator for neural networks with the mixed time-varying delays are investigated by constructing appropriate Lyapunov-Krasovskii functionals and using some effective mathematical techniques. In order to derive several conditions to guarantee the estimation error systems to be globally exponential stable, we transform the considered systems into the neural-type time-delay systems. Then with a set of linear inequalities(LMIs), we can obtain the stable criteria. Finally, three numerical examples are given to show the effectiveness and less conservatism of the proposed criterion

Stability Criteria for Neural Networks with Two Additive Time-varying Delay Components

This paper is concerned with the stability problem with two additive time-varying delay components. By choosing one augmented Lyapunov-Krasovskii functional, using some new zero equalities, and combining linear matrix inequalities (LMI) techniques, two new sufficient criteria ensuring the global stability asymptotic stability of DNNs is obtained. These stability criteria are present in terms of linear matrix inequalities and can be easily checked. Finally, some examples are showed to demonstrate the effectiveness and less conservatism of the proposed method

Stability Criteria for Neural Networks with Two Additive Time-varying Delay Components

This paper is concerned with the stability problem with two additive time-varying delay components. By choosing one augmented Lyapunov-Krasovskii functional, using some new zero equalities, and combining linear matrix inequalities (LMI) techniques, two new sufficient criteria ensuring the global stability asymptotic stability of DNNs is obtained. These stability criteria are present in terms of linear matrix inequalities and can be easily checked. Finally, some examples are showed to demonstrate the effectiveness and less conservatism of the proposed method

New Stability Criterion for Takagi-Sugeno Fuzzy Cohen-Grossberg Neural Networks with Probabilistic Time-Varying Delays

A new global asymptotic stability criterion of Takagi-Sugeno fuzzy Cohen-Grossberg neural networks with probabilistic time-varying delays was derived, in which the diffusion item can play its role. Owing to deleting the boundedness conditions on amplification functions, the main result is a novelty to some extent. Besides, there is another novelty in methods, for Lyapunov-Krasovskii functional is the positive definite form of p powers, which is different from those of existing literature. Moreover, a numerical example illustrates the effectiveness of the proposed methods

Robust exponential stability of nonlinear impulsive switched systems with time-varying delays

This paper deals with a class of uncertain nonlinear impulsive switched systems with time-varying delays. A novel type of piecewise Lyapunov functionals is constructed to derive the exponential stability. This type of functionals can efficiently overcome the impulsive and switching jump of adjacent Lyapunov functionals at impulsive switching times. Based on this, a delay-independent sufficient condition of exponential stability is presented by minimum dwell time. Finally, an illustrative numerical example is given to show the effectiveness of the obtained theoretical results

LMI Approach to Exponential Stability and Almost Sure Exponential Stability for Stochastic Fuzzy Markovian-Jumping Cohen-Grossberg Neural Networks with Nonlinear p-Laplace Diffusion

The robust exponential stability of delayed fuzzy Markovian-jumping Cohen-Grossberg neural networks (CGNNs) with nonlinear p-Laplace diffusion is studied. Fuzzy mathematical model brings a great difficulty in setting up LMI criteria for the stability, and stochastic functional differential equations model with nonlinear diffusion makes it harder. To study the stability of fuzzy CGNNs with diffusion, we have to construct a Lyapunov-Krasovskii functional in non-matrix form. But stochastic mathematical formulae are always described in matrix forms. By way of some variational methods in W1,p(Ω), Itô formula, Dynkin formula, the semi-martingale convergence theorem, Schur Complement Theorem, and LMI technique, the LMI-based criteria on the robust exponential stability and almost sure exponential robust stability are finally obtained, the feasibility of which can efficiently be computed and confirmed by computer MatLab LMI toolbox. It is worth mentioning that even corollaries of the main results of this paper improve some recent related existing results. Moreover, some numerical examples are presented to illustrate the effectiveness and less conservatism of the proposed method due to the significant improvement in the allowable upper bounds of time delays

Coefficient Matrix Decomposition Method and BIBO Stabilization of Stochastic Systems with Time Delays

The mean square BIBO stabilization is investigated for the stochastic control systems with time delays and nonlinear perturbations. A class of suitable Lyapunov functional is constructed, combined with the descriptor model transformation and the decomposition technique of coefficient matrix; thus some novel delay-dependent mean square BIBO stabilization conditions are derived. These conditions are expressed in the forms of linear matrix inequalities (LMIs), whose feasibility can be easily checked by using Matlab LMI Toolbox. Finally, three numerical examples are given to demonstrate that the derived conditions are effective and much less conservative than those given in the literature

Robust Stability of Switched Delay Systems with Average Dwell Time under Asynchronous Switching

The problem of robust stability of switched delay systems with average dwell time under asynchronous switching is investigated. By taking advantage of the average dwell-time method and an integral inequality, two sufficient conditions are developed to guarantee the global exponential stability of the considered switched system. Finally, a numerical example is provided to demonstrate the effectiveness and feasibility of the proposed techniques

Existence and Multiple Positive Solutions for Boundary Value Problem of Fractional Differential Equation with p

This paper investigates the existence, multiplicity, nonexistence, and uniqueness of positive solutions to a kind of two-point boundary value problem for nonlinear fractional differential equations with p-Laplacian operator. By using fixed point techniques combining with partially ordered structure of Banach space, we establish some criteria for existence and uniqueness of positive solution of fractional differential equations with p-Laplacian operator in terms of different value of parameter. In particular, the dependence of positive solution on the parameter was obtained. Finally, several illustrative examples are given to support the obtained new results. The study of illustrative examples shows that the obtained results are applicable