State estimation for discrete-time neural networks with Markov-mode-dependent lower and upper bounds on the distributed delays

Copyright @ 2012 Springer VerlagThis paper is concerned with the state estimation problem for a new class of discrete-time neural networks with Markovian jumping parameters and mixed time-delays. The parameters of the neural networks under consideration switch over time subject to a Markov chain. The networks involve both the discrete-time-varying delay and the mode-dependent distributed time-delay characterized by the upper and lower boundaries dependent on the Markov chain. By constructing novel Lyapunov-Krasovskii functionals, sufficient conditions are firstly established to guarantee the exponential stability in mean square for the addressed discrete-time neural networks with Markovian jumping parameters and mixed time-delays. Then, the state estimation problem is coped with for the same neural network where the goal is to design a desired state estimator such that the estimation error approaches zero exponentially in mean square. The derived conditions for both the stability and the existence of desired estimators are expressed in the form of matrix inequalities that can be solved by the semi-definite programme method. A numerical simulation example is exploited to demonstrate the usefulness of the main results obtained.This work was supported in part by the Royal Society of the U.K., the National Natural Science Foundation of China under Grants 60774073 and 61074129, and the Natural Science Foundation of Jiangsu Province of China under Grant BK2010313

Stability and synchronization of discrete-time Markovian jumping neural networks with mixed mode-dependent time delays

Copyright [2009] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, we introduce a new class of discrete-time neural networks (DNNs) with Markovian jumping parameters as well as mode-dependent mixed time delays (both discrete and distributed time delays). Specifically, the parameters of the DNNs are subject to the switching from one to another at different times according to a Markov chain, and the mixed time delays consist of both discrete and distributed delays that are dependent on the Markovian jumping mode. We first deal with the stability analysis problem of the addressed neural networks. A special inequality is developed to account for the mixed time delays in the discrete-time setting, and a novel Lyapunov-Krasovskii functional is put forward to reflect the mode-dependent time delays. Sufficient conditions are established in terms of linear matrix inequalities (LMIs) that guarantee the stochastic stability. We then turn to the synchronization problem among an array of identical coupled Markovian jumping neural networks with mixed mode-dependent time delays. By utilizing the Lyapunov stability theory and the Kronecker product, it is shown that the addressed synchronization problem is solvable if several LMIs are feasible. Hence, different from the commonly used matrix norm theories (such as the M-matrix method), a unified LMI approach is developed to solve the stability analysis and synchronization problems of the class of neural networks under investigation, where the LMIs can be easily solved by using the available Matlab LMI toolbox. Two numerical examples are presented to illustrate the usefulness and effectiveness of the main results obtained

Time-and event-driven communication process for networked control systems: A survey

Copyright © 2014 Lei Zou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.In recent years, theoretical and practical research topics on networked control systems (NCSs) have gained an increasing interest from many researchers in a variety of disciplines owing to the extensive applications of NCSs in practice. In particular, an urgent need has arisen to understand the effects of communication processes on system performances. Sampling and protocol are two fundamental aspects of a communication process which have attracted a great deal of research attention. Most research focus has been on the analysis and control of dynamical behaviors under certain sampling procedures and communication protocols. In this paper, we aim to survey some recent advances on the analysis and synthesis issues of NCSs with different sampling procedures (time-and event-driven sampling) and protocols (static and dynamic protocols). First, these sampling procedures and protocols are introduced in detail according to their engineering backgrounds as well as dynamic natures. Then, the developments of the stabilization, control, and filtering problems are systematically reviewed and discussed in great detail. Finally, we conclude the paper by outlining future research challenges for analysis and synthesis problems of NCSs with different communication processes.This work was supported in part by the National Natural Science Foundation of China under Grants 61329301, 61374127, and 61374010, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

Stability Analysis of Delayed Genetic Regulatory Networks via a Relaxed Double Integral Inequality

Time delay arising in a genetic regulatory network may cause the instability. This paper is concerned with the stability analysis of genetic regulatory networks with interval time-varying delays. Firstly, a relaxed double integral inequality, named as Wirtinger-type double integral inequality (WTDII), is established to estimate the double integral term appearing in the derivative of Lyapunov-Krasovskii functional with a triple integral term. And it is proved theoretically that the proposed WTDII is tighter than the widely used Jensen-based double inequality and the recently developed Wiringter-based double inequality. Then, by applying the WTDII to the stability analysis of a delayed genetic regulatory network, together with the usage of useful information of regulatory functions, several delay-range- and delay-rate-dependent (or delay-rate-independent) criteria are derived in terms of linear matrix inequalities. Finally, an example is carried out to verify the effectiveness of the proposed method and also to show the advantages of the established stability criteria through the comparison with some literature

Event-triggered distributed H∞ state estimation with packet dropouts through sensor networks

This study is concerned with the event-triggered distributed H∞ state estimation problem for a class of discrete-time stochastic non-linear systems with packet dropouts in a sensor network. An event-triggered communication mechanism is adopted over the sensor network with hope to reduce the communication burden and the energy consumption, where the measurements on each sensor are transmitted only when a certain triggering condition is violated. Furthermore, a novel distributed state estimator is designed where the available innovations are not only from the individual sensor, but also from its neighbouring ones according to the given topology. The purpose of the problem under consideration is to design a set of distributed state estimators such that the dynamics of estimation errors is exponentially mean-square stable and also the prespecified H∞ disturbance rejection attenuation level is guaranteed. By utilising the property of the Kronecker product and the stochastic analysis approaches, sufficient conditions are established under which the addressed state estimation problem is recast as a convex optimisation one that can be easily solved via available software packages. Finally, a simulation example is utilised to illustrate the usefulness of the proposed design scheme of event-triggered distributed state estimators.This work was supported in part by Royal Society of the UK, the National Natural Science Foundation of China under Grants 61329301, 61203139, 61473076, 61374127 and 61422301, the Shanghai Rising-Star Program of China under Grant 13QA1400100, the ShuGuang project of Shanghai Municipal Education Commission and Shanghai Education Development Foundation under Grant 13SG34, the Fundamental Research Funds for the Central Universities, DHU Distinguished Young Professor Program, and the Alexander von Humboldt Foundation of Germany

State Estimation for Discrete-Time Fuzzy Cellular Neural Networks with Mixed Time Delays

This paper is concerned with the exponential state estimation problem for a class of discrete-time fuzzy cellular neural networks with mixed time delays. The main purpose is to estimate the neuron states through available output measurements such that the dynamics of the estimation error is globally exponentially stable. By constructing a novel Lyapunov-Krasovskii functional which contains a triple summation term, some sufficient conditions are derived to guarantee the existence of the state estimator. The linear matrix inequality approach is employed for the first time to deal with the fuzzy cellular neural networks in the discrete-time case. Compared with the present conditions in the form of M-matrix, the results obtained in this paper are less conservative and can be checked readily by the MATLAB toolbox. Finally, some numerical examples are given to demonstrate the effectiveness of the proposed results