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This paper is concerned with the problem of delay-dependent stability of delayed generalized continuous neural networks, which include two classes of fundamental neural networks, i.e., static neural networks and local field neural networks, as their special cases. It is assumed that the state delay belongs to a given interval, which means that the lower bound of delay is not restricted to be zero. An improved integral inequality lemma is proposed to handle the cross-product terms occurred in derivative of constructed Lyapunov–Krasovskii functional. By using the new lemma and delay partitioning method, some less conservative stability criteria are obtained in terms of LMIs. Numerical examples are finally given to illustrate the effectiveness of the proposed method over the existing ones. [ABSTRACT FROM AUTHOR]

Abstract: This paper studies the problem of state estimation for static neural networks with time-varying delay. By construction of a suitable Lyapunov–Krasovskii functional, some improved delay-dependent conditions are established such that the error system is globally exponentially stable with a decay rate and a prescribed performance is guaranteed. In order to get less conservative results of the state estimation condition, zero equalities and reciprocally convex approach are employed. The estimator gain matrix can be obtained in terms of the solution to linear matrix inequalities. Numerical examples are provided to illustrate the effectiveness and performance of the developed method. [Copyright &y& Elsevier]

In this paper, we investigate the problem of ℋ∞ synchronization for chaotic neural networks with time-varying delays. A new model of the networks with disturbances in both master and slave systems is presented. By constructing a suitable Lyapunov—Krasovskii functional and using a reciprocally convex approach, a novel ℋ∞ synchronization criterion for the networks concerned is established in terms of linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. Two numerical examples are given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: This paper concerns the problem of delay-dependent stability criteria for neural networks with interval time-varying delays. First, by constructing a newly augmented Lyapunov–Krasovskii functional and combining with a reciprocally convex combination technique, less conservative stability criterion is established in terms of linear matrix inequalities (LMIs), which will be introduced in . Second, by taking different interval of integral terms of Lyapunov–Krasovskii functional utilized in , further improved stability criterion is proposed in . Third, a novel approach which divides the bounding of activation function into two subinterval are proposed in to reduce the conservatism of stability criterion. Finally, through two well-known numerical examples used in other literature, it will be shown the proposed stability criteria achieves the improvements over the existing ones and the effectiveness of the proposed idea. [Copyright &y& Elsevier]

Abstract: This paper deals with the absolute stability analysis for uncertain time delay Lur’e systems that have time-varying delays and sector and slope restricted nonlinearities. New delay-dependent stability criteria are derived via linear matrix inequality (LMI) formulation that can be easily solved by various optimization techniques. Sector bounds and slope bounds are employed to the Lyapunov–Krasovskii functional through convex representation of the nonlinearities so that less conservative stability conditions are obtained. Numerical examples show effectiveness of the proposed stability condition. [Copyright &y& Elsevier]

Abstract: This paper considers the problem of robust stability analysis for uncertain Takagi–Sugeno (T–S) fuzzy systems with time-varying delays. By constructing an augmented Lyapunov–Krasovskii functional and utilizing Finsler''s Lemma, a novel criterion for delay-dependent robust stability of T–S fuzzy model with time-varying delay is derived in terms of linear matrix inequalities (LMIs). Also, a further improved stability criterion is proposed by utilizing free weighting techniques. Finally, three numerical examples are included to show the superiority of the proposed criteria. [Copyright &y& Elsevier]

Abstract: In this paper, the problem of delay-dependent stability for uncertain neutral systems with time-varying delays is considered. The parameter uncertainties are assumed to be norm-bounded. By constructing an augmented Lyapunov functionals, a novel delay-dependent stability criterion for the system is established in terms of LMIs (linear matrix inequalities). Six numerical examples are given to show the effectiveness of proposed method. [Copyright &y& Elsevier]

Abstract: This paper proposes a new consensus criterion for discrete-time multi-agent systems with communication-delay and disturbances. By constructing a suitable Lyapunov–Krasovskii (L–K) functional, which fractionizes the delay interval into two subsections, and utilizing reciprocally convex approach, a new consensus criterion for the concerned systems is established in terms of linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. One numerical example is given to illustrate the effectiveness of the proposed method. [Copyright &y& Elsevier]

Abstract: In this paper, the problem of stability analysis for static neural networks with interval time-varying delays is considered. By the consideration of new augmented Lyapunov functionals, new and improved delay-dependent stability criteria to guarantee the asymptotic stability of the concerned networks are proposed with the framework of linear matrix inequalities (LMIs), which can be solved easily by standard numerical packages. The enhancement of the feasible region of the proposed criteria is shown via two numerical examples by the comparison of maximum delay bounds. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to investigate the delay-dependent synchronization analysis for coupled discrete-time neural networks with interval time-varying delays in network couplings. Based on Lyapunov method, a new delay-dependent criterion for the synchronization of the networks is derived in terms of linear matrix inequalities (LMIs) by construction of a suitable Lyapunov–Krasovskii''s functional and utilization of Finsler''s lemma without free-weighting matrices. Two numerical examples are given to illustrate the effectiveness of the proposed method. [Copyright &y& Elsevier]

Abstract: This paper presents new delay-dependent synchronization criteria for fuzzy complex dynamical networks with interval time-varying delays. By construction of a suitable Lyapunov–Krasovskii’s (L–K) functional and utilization of Finsler’s lemma, new synchronization criteria for the networks are established in terms of linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. One numerical example is given to illustrate the effectiveness of the proposed methods. [Copyright &y& Elsevier]

Abstract: This paper proposes delay-dependent stability conditions of fuzzy Markovian jumping Hopfield neural networks of neutral type with interval time-varying delays. By constructing a suitable Lyapunov–Krasovskii’s functional and utilizing Finsler’s lemma with no free weighting matrices, new delay-dependent stability criteria for the networks are established in terms of linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. Numerical examples is given to illustrate the effectiveness of the proposed methods. [Copyright &y& Elsevier]

Abstract: This paper proposes improved delay-dependent conditions for asymptotic stability of linear systems with time-varying delays. The proposed method employs a suitable Lyapunov–Krasovskii’s functional for new augmented system. Based on Lyapunov method, delay-dependent stability criteria for the systems are established in terms of linear matrix inequalities (LMIs) which can be easily solved by various optimization algorithms. Three numerical examples are included to show that the proposed method is effective and can provide less conservative results. [Copyright &y& Elsevier]

• This paper proposes a new stability analysis method for time delay systems by using an augmented zero equality. • An improved stability condition of systems is introduced by the use of Finsler's Lemma and an augmented zero equality. • In numerical examples, the maximum bounds of time-delay demonstrate the superiority of the proposed method. This work focuses the delay-dependent stability problem for linear systems with time-varying delays. By composing a suitable augmented Lyapunov–Krasovskii functionals, using recent developed integral inequality and choosing newly states, a set of sufficient conditions for stability condition is induced within framework of linear matrix inequalities (LMIs). To enhance the feasible region of stability, single augmented zero equality is established with the augmented state vectors for the first time and the equality constraint is incorporated into a simple stability criterion by utilizing Finsler's lemma. The comparison of maximum bounds of time-delay with various results proposed by recent studies will be conducted in numerical examples to demonstrate the superiority of the theorems presented by this paper. [ABSTRACT FROM AUTHOR]