Delay-dependent Exponential Stability Research Articles

Robust exponential stability criteria of uncertain stochastic systems with time-varying delays

This article investigates the problem of delay-dependent exponential stability in mean square for continuous-time linear stochastic systems with structured uncertainties and time-varying delays. By applying descriptor model transformation of the systems, a new type of Lyapunov–Krasovskii functional is constructed, and by introducing some free weighting matrices, some new delay-dependent and delay-independent stability criteria are derived respectively in terms of an LMI algorithm. The new stability criteria are less conservative than existing results. Numerical examples demonstrate that the new criteria are effective and are an improvement over existing results.

Delay-dependent exponential stability analysis for discrete-time switched neural networks with time-varying delay

In this paper, we focus on the stability problem for discrete-time switched neural networks with time-varying delay resorting to the average dwell time method. In terms of linear matrix inequality approach, a delay-dependent sufficient condition of exponential stability is developed for a kind of switching signal with average dwell time. A numerical example is given to show the validness of the established result.

Robust delay-dependent exponential stability for uncertain stochastic neural networks with mixed delays

This paper is concerned with the robust delay-dependent exponential stability of uncertain stochastic neural networks (SNNs) with mixed delays. Based on a novel Lyapunov–Krasovskii functional method, some new delay-dependent stability conditions are presented in terms of linear matrix inequalities, which guarantee the uncertain stochastic neural networks with mixed delays to be robustly exponentially stable. Numerical examples are given to illustrate the effectiveness of our results.

Delay-dependent exponential stabilization for uncertain linear systems with interval non-differentiable time-varying delays

In this paper, the problem of exponential stabilization for a class of linear systems with time-varying delay is studied. The time delay is a continuous function belonging to a given interval, which means that the lower and upper bounds for the time-varying delay are available, but the delay function is not necessary to be differentiable. Based on the construction of improved Lyapunov–Krasovskii functionals combined with Leibniz–Newton’s formula, new delay-dependent sufficient conditions for the exponential stabilization of the systems are first established in terms of LMIs. Numerical examples are given to demonstrate that the derived conditions are much less conservative than those given in the literature.

Global exponential stability of reaction—diffusion neural networks with discrete and distributed time-varying delays**Project partially supported by the National Natural Science Foundation of China (Grant No. 60974139) and partially supported by the Fundamental Research Funds for the Central Universities.

This paper investigates the global exponential stability of reaction—diffusion neural networks with discrete and distributed time-varying delays. By constructing a more general type of Lyapunov—Krasovskii functional combined with a free-weighting matrix approach and analysis techniques, delay-dependent exponential stability criteria are derived in the form of linear matrix inequalities. The obtained results are dependent on the size of the time-varying delays and the measure of the space, which are usually less conservative than delay-independent and space-independent ones. These results are easy to check, and improve upon the existing stability results. Some remarks are given to show the advantages of the obtained results over the previous results. A numerical example has been presented to show the usefulness of the derived linear matrix inequality (LMI)-based stability conditions.

Improved delay-dependent stability criteria for discrete-time stochastic neural networks with time-varying delays

This letter, investigates the problem of mean square exponential stability for a class of discrete-time stochastic neural network with time-varying delays. By constructing a appropriate Lyapunov-Krasovskii functional, combining the stochastic stability theory, and the convex theory method, a delay-dependent exponential stability criteria is obtained in term of LMIs. Finally, a numerical example is exploited to show the usefulness of the results derived.

A new delay-dependent exponential stability criterion for Itô stochastic systems with Markovian switching and time-varying delay

On the basis of the Lyapunov–Krasovskii method, the exponential stability in the mean square sense is investigated for Itô stochastic systems with Markovian switching and time-varying delay. The statistic properties of the Markov process and Brownian motion are employed to compute the constructed Lyapunov–Krasovskii functional of a rather general form. This enables us to make sense of the challenging problems in the stochastic framework, and then find a way to extend the techniques developed in the deterministic framework. Therefore, the stability conditions are established with the aid of some slack matrices and the boundary conditions on time-varying delay. Numerical examples are given to demonstrate the reduced conservatism.

An improved exponential stability criterion for a class of neutral delayed differential equations

In this letter, a new sufficient delay-dependent exponential stability condition for a class of neutral delayed differential equations: d d t [ x ( t ) + p x ( t − τ ( t ) ) ] + a x ( t ) − b tanh x ( t − σ ( t ) ) = 0 , is given in terms of the linear matrix inequality (LMI). Our delay-dependent condition obtained here is shown to be less conservative than some existing results via three illustrative examples.

Exponential Convergence Rate Estimation for a Class of BAM Neural Networks with Time-Delays

This paper is concerned with the exponential stability analysis problem for a class of neutral bidirectional associative memory (BAM) neural networks with parameter uncertainties and mixed time-delays where the parameter uncertainties are norm-bounded and the mixed time-delays involve discrete, distributed and neutral time-delays. By utilizing free-weighting matrix method and an appropriately constructed Lyapunov-Krasovskii Functional, some nove delay-dependent and decay-rate dependent exponential stability criteria are derived in the terms of linear matrix inequalities (LMIs). Meanwhile, the maximum allowable decay rate can be estimated based on the obtained results. Two numerical examples are presented to demonstrate the effectiveness of the proposed method.

Robust exponential stability and stabilizability of linear parameter dependent systems with delays

The robust exponential stability and stabilizability problems are addressed in this paper for a class of linear parameter dependent systems with interval time-varying and constant delays. In this paper, restrictions on the derivative of the time-varying delay is not required which allows the time-delay to be a fast time-varying function. Based on the Lyapunov–Krasovskii theory, we derive delay-dependent exponential stability and stabilizability conditions in terms of linear matrix inequalities (LMIs) which can be solved by various available algorithms. Numerical examples are given to illustrate the effectiveness of our theoretical results.

Delay-dependent exponential stability for impulsive Cohen–Grossberg neural networks with time-varying delays and reaction–diffusion terms

In this paper, a class of impulsive Cohen–Grossberg neural networks with time-varying delays and reaction–diffusion is formulated and investigated. By employing delay differential inequality and the linear matrix inequality (LMI) optimization approach, some sufficient conditions ensuring global exponential stability of equilibrium point for impulsive Cohen–Grossberg neural networks with time-varying delays and diffusion are obtained. In particular, the estimate of the exponential convergence rate is also provided, which depends on system parameters, diffusion effect and impulsive disturbed intention. It is believed that these results are significant and useful for the design and applications of Cohen–Grossberg neural networks. An example is given to show the effectiveness of the results obtained here.

Robust Exponential Stability of Uncertain Singular Markovian Jump Time-delay Systems

In this paper,the problem of delay-dependent robust exponential stability is investigated for uncertain singular Marko- vian jump systems with time delay.A delay-range-dependent condition is given which ensures that the nominal system is regular,impulse free,and mean-square exponentially stable in terms of linear matrix inequality (LMI) approach.The criterion is also extended to uncertain case.Numerical examples are given to show that the proposed criteria improve the existing results.

Stabilization analysis for discrete-time systems with time delay

The stabilization problem for a class of discrete-time systems with time-varying delay is investigated. By constructing an augmented Lyapunov function, some sufficient conditions guaranteeing exponential stabilization are established in forms of linear matrix inequality (LMI) technique. When norm-bounded parameter uncertainties appear in the delayed discrete-time system, a delay-dependent robust exponential stabilization criterion is also presented. All of the criteria obtained in this paper are strict linear matrix inequality conditions, which make the controller gain matrix can be solved directly. Three numerical examples are provided to demonstrate the effectiveness and improvement of the derived results.

Robust Delay-dependent Exponential Stability of Uncertain Stochastic System with Time-varying Delay

This paper discusses the problem of robust delay-dependent exponential stability for a class of uncertain stochastic systems with time-varying delay. The uncertainty is assumed to be of norm-bounded form. A less conservative robust exponential stability condition is derived by using a new Lyapunov–Krasovskii functional and a free-weighting matrix method in terms of linear matrix inequalities. Two numerical examples are given to illustrate the effectiveness of the proposed method.

Improved delay-dependent exponential stability for uncertain stochastic neural networks with time-varying delays

This Letter investigates the problem of delay-dependent exponential stability analysis for uncertain stochastic neural networks with time-varying delay. Based on the Lyapunov stability theory, improved delay-dependent exponential stability criteria for the networks are established in terms of linear matrix inequalities (LMIs).

Delay-dependent exponential stability for neural networks with discrete and distributed time-varying delays

This Letter studies the exponential stability for a class of neural networks (NNs) with both discrete and distributed time-varying delays. Under weaker assumptions on the activation functions, by defining a more general type of Lyapunov functionals and developing a new convex combination technique, new less conservative and less complex stability criteria are established to guarantee the global exponential stability of the discussed NNs. The obtained conditions are dependent on both discrete and distributed delays, are expressed in terms of linear matrix inequalities (LMIs), and contain fewer decision variables. Numerical examples are given to illustrate the effectiveness and the less conservatism of the proposed conditions.

Delay-dependent exponential stability criteria for stochastic systems with polytopic-type uncertainties

This paper considers the problem of delay-dependent exponential stability in mean square for stochastic systems with polytopic-type uncertainties and time-varying delay. Applying the descriptor model transformation and introducing free weighting matrices, a new type of Lyapunov-Krasovskii functional is constructed based on linear matrix inequalities (LMIs), and some new delay-dependent criteria are obtained. These criteria include the delay-independent/ratedependent and delay-dependent/rate-independent exponential stability criteria. These new criteria are less conservative than existing ones. Numerical examples demonstrate that these new criteria are effective and are an improvement over existing ones.

Delay-dependent robust exponential stabilization for uncertain systems with interval time-varying delays

New robust exponential stabilization criteria for interval time-varying delay systems with norm-bounded uncertainties are proposed. Based on the free-weighting matrices and new Lyapunov-Krasovskii functionals, such criteria are obtained by dealing with system model directly and designing memoryless state feedback controllers and expressed in terms of linear matrix inequalities (LMIs). Moreover, the criteria are applicable to the case whether the derivative of the time-varying delay is bounded or not. The state decay rate is estimated by the corresponding LMIs. Numerical examples are given to illustrate the effectiveness of the proposed method.

Correction to: "Delay-Dependent Exponential Stability of Neutral Stochastic Delay Systems" [Jan 09 147-152

In the above titled paper (ibid., vol. 54, no. 1, pp. 147-152), there were some typographical errors in inequalities. Corrections are presented here.

Delay-Dependent Exponential Stability for Uncertain Stochastic Hopfield Neural Networks With Time-Varying Delays

This paper provides new delay-dependent conditions that guarantee the robust exponential stability of stochastic Hopfield type neural networks with time-varying delays and parameter uncertainties. Both the cases of the time-varying delays which are differentiable and may not be differentiable are considered. The stability conditions are derived by using the recently developed free-weighting matrices technique and expressed in terms of linear matrix inequalities. Numerical examples are provided to demonstrate the effectiveness of the proposed stability criteria. It is shown that the proposed stability results are less conservative than some previous ones in the literature.