Probabilistic Time-varying Delays Research Articles

Delay-derivative-dependent stability criterion for neural networks with probabilistic time-varying delay

In this article, based on Lyapunov–Krasovskii functional approach and improved delay-partitioning idea, a new sufficient condition is derived to guarantee a class of delayed neural networks to be asymptotically stable in the mean-square sense, in which the probabilistic time-varying delay is addressed. Together with general convex combination method, the criterion is presented via LMIs and its solvability heavily depends on the sizes of both time delay range and its derivative, which has wider application fields than those present ones. It can be shown by the numerical examples that our method reduces the conservatism much more effectively than earlier reported ones. Especially, the conservatism can be further decreased by thinning the delay intervals.

Sampled-data state estimation for Markovian jumping fuzzy cellular neural networks with mode-dependent probabilistic time-varying delays

In this paper, the problem of state estimation for Markovian jumping fuzzy cellular neural networks (FCNNs) using sampled-data with mode-dependent probabilistic time-varying delays is investigated. By developing a delay decomposition approach, the information of the delayed states can be taken into full consideration. By introducing a stochastic variable with a Bernoulli distribution, the information of probability distribution of the time-varying delay is considered and transformed into one with deterministic time-varying delay. The main purpose of this paper is to estimate the neuron states through available output measurements such that the dynamics of the estimation error is globally asymptotically stable in the mean square. Based on the Lyapunov–Krasovskii functional including triple integral terms and decomposed integral intervals, delay-distribution-dependent stability criteria are obtained in terms of linear matrix inequalities (LMIs). Finally two numerical examples are given to illustrate the effectiveness of the proposed theoretical results.

Stability and Stabilization for Discrete System With Probabilistic Nonlinearities

This paper investigates stability and stabilization of discrete systems with probabilistic nonlinearities and time-varying delay. New characters of the nonlinearities, the probability of the nonlinearities happening between different bounds, are used to build new type of system model, which can help us make a full use of the inner variation information of the nonlinearities. With the help of the new characters, new system model is proposed. Then, sufficient conditions for the mean square stability of the system can be obtained by using the Lyapunov functional approach and linear matrix inequalities technique. An example is proposed to illustrate the efficiency of the proposed method.

Stability criteria for BAM neural networks with leakage delays and probabilistic time-varying delays

This paper is concerned with the stability criteria for bidirectional associative memory (BAM) neural networks with leakage time delay and probabilistic time-varying delays. By establishing a stochastic variable with Bernoulli distribution, the information of probabilistic time-varying delay is transformed into the deterministic time-varying delay with stochastic parameters. Based on the Lyapunov–Krasovskii functional and stochastic analysis approach, delay-probability-distribution-dependent sufficient conditions are derived to achieve the globally asymptotically mean square stable of the considered BAM neural networks. The criteria are formulated in terms of a set of linear matrix inequalities (LMIs), which can be checked efficiently by use of some standard numerical packages. Finally, a numerical example and its simulations are given to demonstrate the usefulness and effectiveness of the proposed results.

Delay-dependent absolute stability criterion for Lurie system with probabilistic interval time-varying delay

In this paper, the absolute stability of Lurie control system with probabilistic time-varying delay is studied. By using a new extended Lyapunov-Krasovskii functional, an improved stability criterion based on LMIs is presented and its solvability heavily depends on the sizes of both the delay range and its derivatives, which has wider application fields than those present results. The efficiency and reduced conservatism of the presented results can be demonstrated by two numerical examples with giving some comparing results.

Delay-distribution-dependent Robust Stability Analysis of Uncertain Lurie Systems with Time-varying Delay

AbstractIn this paper, the problem of robust absolute stability of Lurie system with probabilistic time-varying delay and norm-bounded parametric uncertainty is considered. The time delay variation range is divided into two subintervals. By considering the probability distribution of the time-varying delay between the two subintervals and the knowledge of the delay variation range, a novel linear matrix inequalities (LMIs) based stability condition is derived by defining a Lyapunov Krasovskii functional. It is illustrated with the help of numerical examples that the derived stability criteria can lead to less conservative results as compared to the results obtained by the traditional method of using the delay variation range information only.

CLUSTER SYNCHRONIZATION OF DISCRETE-TIME STOCHASTIC COMPLEX DYNAMICAL NETWORKS WITH PROBABILISTIC INTERVAL TIME-VARYING DELAYS

The paper investigates the cluster synchronization in discrete-time complex networks with stochastic nonlinearities and probabilistic interval time-varying delays. Based on the stochastic analysis techniques and the properties of the Kronecker product, delay-dependent cluster synchronization stability criteria are derived in the form of linear matrix inequalities. The solvability of derived conditions depends on not only the probability of the binary switch between nonlinear functions, but also the size of the delay and the probability of the delay taking values in some intervals. Finally, a numerical simulation is provided to illustrate the effectiveness of the proposed criterion.