6 results on '"Yurong Liu"'
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2. Stability and synchronization of discrete-time Markovian jumping neural networks with mixed mode-dependent time delays
- Author
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Yurong, Liu, Zidong, Wang, Jinling, Liang, and Xiaohui, Liu
- Subjects
Business ,Computers ,Electronics ,Electronics and electrical industries - Abstract
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. Index Terms--Discrete-time neural networks (DNNs), linear matrix inequality, Markovian jumping parameters, mixed time delays, stochastic stability, synchronization.
- Published
- 2009
3. Stability and Synchronization of Discrete-Time Markovian Jumping Neural Networks With Mixed Mode-Dependent Time Delays
- Author
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Jinling Liang, Xiaohui Liu, Yurong Liu, and Zidong Wang
- Subjects
Lyapunov function ,Mathematical optimization ,Time Factors ,Computer Networks and Communications ,Software Validation ,Markovian jumping parameters ,Markov process ,Synchronization ,Discrete-time neural networks (DNNs) ,Stochastic stability ,symbols.namesake ,Artificial Intelligence ,Control theory ,Mixed time delays ,Computer Simulation ,Mathematical Computing ,Mathematics ,Kronecker product ,Lyapunov stability ,Stochastic Processes ,Artificial neural network ,Linear matrix inequality ,General Medicine ,Markov Chains ,Computer Science Applications ,Linear matrix inequality Markovian jumping parameters ,Discrete time and continuous time ,Linear Models ,symbols ,Neural Networks, Computer ,Algorithms ,Software - Abstract
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 pubs-permissions@ieee.org. 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.
- Published
- 2009
4. Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays
- Author
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Maozhen Li, Xiaohui Liu, Yurong Liu, and Zidong Wang
- Subjects
Equilibrium point ,Stochastic Processes ,Models, Statistical ,Time Factors ,Artificial neural network ,Computer Networks and Communications ,Stochastic process ,Linear matrix inequality ,Information Storage and Retrieval ,Systems Theory ,General Medicine ,Stability (probability) ,Pattern Recognition, Automated ,Computer Science Applications ,Exponential stability ,Computer Science::Systems and Control ,Artificial Intelligence ,Control theory ,Stability theory ,Convergence (routing) ,Computer Simulation ,Neural Networks, Computer ,Algorithms ,Software ,Mathematics - Abstract
In this letter, the global asymptotic stability analysis problem is considered for a class of stochastic Cohen-Grossberg neural networks with mixed time delays, which consist of both the discrete and distributed time delays. Based on an Lyapunov-Krasovskii functional and the stochastic stability analysis theory, a linear matrix inequality (LMI) approach is developed to derive several sufficient conditions guaranteeing the global asymptotic convergence of the equilibrium point in the mean square. It is shown that the addressed stochastic Cohen-Grossberg neural networks with mixed delays are globally asymptotically stable in the mean square if two LMIs are feasible, where the feasibility of LMIs can be readily checked by the Matlab LMI toolbox. It is also pointed out that the main results comprise some existing results as special cases. A numerical example is given to demonstrate the usefulness of the proposed global stability criteria.
- Published
- 2006
5. Robust synchronization of an array of coupled stochastic discrete-time delayed neural networks
- Author
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Jinling Liang, Zidong Wang, Xiaohui Liu, and Yurong Liu
- Subjects
Kronecker product ,Stochastic Processes ,Models, Statistical ,Artificial neural network ,Computer Networks and Communications ,Stochastic process ,Activation function ,Linear matrix inequality ,Signal Processing, Computer-Assisted ,General Medicine ,Synchronization ,Computer Science Applications ,Pattern Recognition, Automated ,symbols.namesake ,Discrete time and continuous time ,Nonlinear Dynamics ,Control theory ,Artificial Intelligence ,symbols ,Computer Simulation ,Neural Networks, Computer ,Stochastic neural network ,Software ,Algorithms ,Mathematics - Abstract
This paper is concerned with the robust synchronization problem for an array of coupled stochastic discrete-time neural networks with time-varying delay. The individual neural network is subject to parameter uncertainty, stochastic disturbance, and time-varying delay, where the norm-bounded parameter uncertainties exist in both the state and weight matrices, the stochastic disturbance is in the form of a scalar Wiener process, and the time delay enters into the activation function. For the array of coupled neural networks, the constant coupling and delayed coupling are simultaneously considered. We aim to establish easy-to-verify conditions under which the addressed neural networks are synchronized. By using the Kronecker product as an effective tool, a linear matrix inequality (LMI) approach is developed to derive several sufficient criteria ensuring the coupled delayed neural networks to be globally, robustly, exponentially synchronized in the mean square. The LMI-based conditions obtained are dependent not only on the lower bound but also on the upper bound of the time-varying delay, and can be solved efficiently via the Matlab LMI Toolbox. Two numerical examples are given to demonstrate the usefulness of the proposed synchronization scheme.
- Published
- 2008
6. Stability Analysis for Stochastic Cohen-Grossberg Neural Networks With Mixed Time Delays.
- Author
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Zidong Wang, Yurong Liu, Maozhen Li, and Xiaohui Liu
- Subjects
- *
STOCHASTIC systems , *STABILITY (Mechanics) , *ARTIFICIAL neural networks , *TIME delay systems , *MATRIX inequalities - Abstract
In this letter, the global asymptotic stability analysis problem is considered for a class of stochastic Cohen-Grossberg neural networks with mixed time delays, which consist of both the discrete and distributed time delays. Based on an Lyapunov-Krasovskii functional and the stochastic stability analysis theory, a linear matrix inequality (LMI) approach is developed to derive several sufficient conditions guaranteeing the global asymptotic convergence of the equilibrium point in the mean square. It is shown that the addressed stochastic Cohen-Grossberg neural networks with mixed delays are globally asymptotically stable in the mean square if two LMIs are feasible, where the feasibility of LMIs can be readily checked by the Matlab LMI toolbox. It is also pointed out that the main results comprise some existing results as special cases. A numerical example is given to demonstrate the usefulness of the proposed global stability criteria. [ABSTRACT FROM AUTHOR]
- Published
- 2006
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