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

Robust H∞ filtering for markovian jump systems with randomly occurring nonlinearities and sensor saturation: The finite-horizon case

This article is posted with the permission of IEEE - Copyright @ 2011 IEEEThis paper addresses the robust H∞ filtering problem for a class of discrete time-varying Markovian jump systems with randomly occurring nonlinearities and sensor saturation. Two kinds of transition probability matrices for the Markovian process are considered, namely, the one with polytopic uncertainties and the one with partially unknown entries. The nonlinear disturbances are assumed to occur randomly according to stochastic variables satisfying the Bernoulli distributions. The main purpose of this paper is to design a robust filter, over a given finite-horizon, such that the H∞ disturbance attenuation level is guaranteed for the time-varying Markovian jump systems in the presence of both the randomly occurring nonlinearities and the sensor saturation. Sufficient conditions are established for the existence of the desired filter satisfying the H∞ performance constraint in terms of a set of recursive linear matrix inequalities. Simulation results demonstrate the effectiveness of the developed filter design scheme.This work was supported in part by the National Natural Science Foundation of China under Grants 61028008, 60825303, and 61004067, National 973 Project under Grant 2009CB320600, the Key Laboratory of Integrated Automation for the Process Industry (Northeastern University) from the Ministry of Education of China, the Engineering and Physical Sciences Research Council (EPSRC) of the U.K., under Grant GR/S27658/01, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany

Synchronization of coupled neutral-type neural networks with jumping-mode-dependent discrete and unbounded distributed delays

This is the post-print version of the Article. The official published version can be accessed from the links below - Copyright @ 2013 IEEE.In this paper, the synchronization problem is studied for an array of N identical delayed neutral-type neural networks with Markovian jumping parameters. The coupled networks involve both the mode-dependent discrete-time delays and the mode-dependent unbounded distributed time delays. All the network parameters including the coupling matrix are also dependent on the Markovian jumping mode. By introducing novel Lyapunov-Krasovskii functionals and using some analytical techniques, sufficient conditions are derived to guarantee that the coupled networks are asymptotically synchronized in mean square. The derived sufficient conditions are closely related with the discrete-time delays, the distributed time delays, the mode transition probability, and the coupling structure of the networks. The obtained criteria are given in terms of matrix inequalities that can be efficiently solved by employing the semidefinite program method. Numerical simulations are presented to further demonstrate the effectiveness of the proposed approach.This work was supported in part by the Royal Society of the U.K., the National Natural Science Foundation of China under Grants 61074129, 61174136 and 61134009, and the Natural Science Foundation of Jiangsu Province of China under Grants BK2010313 and BK2011598

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

Synchronization of stochastic genetic oscillator networks with time delays and Markovian jumping parameters

The official published version of the article can be found at the link below.Genetic oscillator networks (GONs) are inherently coupled complex systems where the nodes indicate the biochemicals and the couplings represent the biochemical interactions. This paper is concerned with the synchronization problem of a general class of stochastic GONs with time delays and Markovian jumping parameters, where the GONs are subject to both the stochastic disturbances and the Markovian parameter switching. The regulatory functions of the addressed GONs are described by the sector-like nonlinear functions. By applying up-to-date ‘delay-fractioning’ approach for achieving delay-dependent conditions, we construct novel matrix functional to derive the synchronization criteria for the GONs that are formulated in terms of linear matrix inequalities (LMIs). Note that LMIs are easily solvable by the Matlab toolbox. A simulation example is used to demonstrate the synchronization phenomena within biological organisms of a given GON and therefore shows the applicability of the obtained results.This work was supported in part by the Biotechnology and Biological Sciences Research Council (BBSRC) of the UK under Grants BB/C506264/1 and 100/EGM17735, the Royal Society of the UK, the National Natural Science Foundation of China under Grant 60804028, the Teaching and Research Fund for Excellent Young Teachers at Southeast University of China, the International Science and Technology Cooperation Project of China under Grant 2009DFA32050, and the Alexander von Humboldt Foundation of Germany

Necessary and sufficient conditions for analysis and synthesis of markov jump linear systems with incomplete transition descriptions

This technical note is concerned with exploring a new approach for the analysis and synthesis for Markov jump linear systems with incomplete transition descriptions. In the study, not all the elements of the transition rate matrices (TRMs) in continuous-time domain, or transition probability matrices (TPMs) in discrete-time domain are assumed to be known. By fully considering the properties of the TRMs and TPMs, and the convexity of the uncertain domains, necessary and sufficient criteria of stability and stabilization are obtained in both continuous and discrete time. Numerical examples are used to illustrate the results. © 2006 IEEE.published_or_final_versio

Finite-time synchronization of Markovian neural networks with proportional delays and discontinuous activations

In this paper, finite-time synchronization of neural networks (NNs) with discontinuous activation functions (DAFs), Markovian switching, and proportional delays is studied in the framework of Filippov solution. Since proportional delay is unbounded and different from infinite-time distributed delay and classical finite-time analytical techniques are not applicable anymore, new 1-norm analytical techniques are developed. Controllers with and without the sign function are designed to overcome the effects of the uncertainties induced by Filippov solutions and further synchronize the considered NNs in a finite time. By designing new Lyapunov functionals and using M-matrix method, sufficient conditions are derived to guarantee that the considered NNs realize synchronization in a settling time without introducing any free parameters. It is shown that, though the proportional delay can be unbounded, complete synchronization can still be realized, and the settling time can be explicitly estimated. Moreover, it is discovered that controllers with sign function can reduce the control gains, while controllers without the sign function can overcome chattering phenomenon. Finally, numerical simulations are given to show the effectiveness of theoretical results

Static output-feedback stabilization of discrete-time Markovian jump linear systems: a system augmentation approach

This paper studies the static output-feedback (SOF) stabilization problem for discrete-time Markovian jump systems from a novel perspective. The closed-loop system is represented in a system augmentation form, in which input and gain-output matrices are separated. By virtue of the system augmentation, a novel necessary and sufficient condition for the existence of desired controllers is established in terms of a set of nonlinear matrix inequalities, which possess a monotonic structure for a linearized computation, and a convergent iteration algorithm is given to solve such inequalities. In addition, a special property of the feasible solutions enables one to further improve the solvability via a simple D-K type optimization on the initial values. An extension to mode-independent SOF stabilization is provided as well. Compared with some existing approaches to SOF synthesis, the proposed one has several advantages that make it specific for Markovian jump systems. The effectiveness and merit of the theoretical results are shown through some numerical example