ON SYNCHRONIZATION OF DISCRETE-TIME MARKOVIAN JUMPING STOCHASTIC COMPLEX NETWORKS WITH MODE-DEPENDENT MIXED TIME-DELAYS

2009 ◽  
Vol 23 (03) ◽  
pp. 411-434 ◽  
Author(s):  
YURONG LIU ◽  
ZIDONG WANG ◽  
XIAOHUI LIU
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Discrete Time ◽  
Time Delays ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Stochastic Disturbances ◽  
Coupling Term ◽  
Markovian Jumping

In this paper, the synchronization problem is investigated for a new class of discrete-time complex networks. Such complex networks involve the Markovian jumping parameters, mode-dependent discrete and distributed time-delays, constant and delayed couplings, as well as multiple stochastic disturbances. The stochastic disturbances influence the constant coupling term, the delayed coupling term, as well as the overall network dynamics, which could better describe the dynamical behavior of a coupled complex network presented within a noisy environment. With help from the Lyapunov functional method and the properties of Kronecker product, we employ the stochastic analysis techniques to derive several delay-dependent sufficient conditions under which the coupled complex network is asymptotically synchronized in the mean square. The criteria obtained in this paper are in the form of LMIs whose solution can be easily calculated using the standard numerical software. It is shown that our main results can cover many existing ones reported in the literature. A numerical example is presented to illustrate the usefulness of our results.

scholarly journals ROBUST SYNCHRONIZATION OF A CLASS OF COUPLED DELAYED NETWORKS WITH MULTIPLE STOCHASTIC DISTURBANCES: THE CONTINUOUS-TIME CASE

2011 ◽  
Vol 25 (06) ◽  
pp. 757-780 ◽  
Author(s):  
JINLING LIANG ◽  
ZIDONG WANG ◽  
XIAOHUI LIU
Keyword(s):  
Complex Network ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Linear Matrix ◽  
Analysis Tool ◽  
Stochastic Disturbances ◽  
Coupling Term ◽  
Parameter Uncertainties ◽  
Robust Synchronization

In this paper, the robust synchronization problem is investigated for a new class of continuous-time complex networks that involve parameter uncertainties, time-varying delays, constant and delayed couplings, as well as multiple stochastic disturbances. The norm-bounded uncertainties exist in all the network parameters after decoupling, and the stochastic disturbances are assumed to be Brownian motions that act on the constant coupling term, the delayed coupling term as well as the overall network dynamics. Such multiple stochastic disturbances could reflect more realistic dynamical behaviors of the coupled complex network presented within a noisy environment. By using a combination of the Lyapunov functional method, the robust analysis tool, the stochastic analysis techniques and the properties of Kronecker product, we derive several delay-dependent sufficient conditions that ensure the coupled complex network to be globally robustly synchronized in the mean square for all admissible parameter uncertainties. The criteria obtained in this paper are in the form of linear matrix inequalities whose solution can be easily calculated by using the standard numerical software. The main results are shown to be general enough to cover many existing ones reported in the literature. Simulation examples are presented to demonstrate the feasibility and applicability of the proposed results.

scholarly journals Global Synchronization of Complex Networks with Discrete Time Delays on Time Scales

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
Quanxin Cheng ◽  
Jinde Cao
Keyword(s):  
Complex Networks ◽  
Time Scales ◽  
Discrete Time ◽  
Time Delays ◽  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Global Synchronization ◽  
Synchronization Problem

This paper studies the global synchronization problem for a class of complex networks with discrete time delays. By using the theory of calculus on time scales, the properties of Kronecker product, and Lyapunov method, some sufficient conditions are obtained to ensure the global synchronization of the complex networks with delays on time scales. These sufficient conditions are formulated in terms of linear matrix inequalities (LMIs). The main contribution of the result is that the global synchronization problems with both discrete time and continuous time are unified under the same framework.

Synchronization for discrete-time complex networks with probabilistic time delays

2019 ◽  
Vol 525 ◽  
pp. 1088-1101 ◽  
Author(s):  
Ranran Cheng ◽  
Mingshu Peng ◽  
Jinchen Yu ◽  
Haifen Li
Keyword(s):  
Complex Networks ◽  
Discrete Time ◽  
Time Delays

Stability analysis for discrete-time stochastic neural networks with mixed time delays and impulsive effects

2010 ◽  
Vol 88 (12) ◽  
pp. 885-898 ◽  
Author(s):  
R. Raja ◽  
R. Sakthivel ◽  
S. Marshal Anthoni
Keyword(s):  
Neural Networks ◽  
Equilibrium Point ◽  
Discrete Time ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Impulsive Effects ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Mixed Time Delays ◽  
The Stability

This paper investigates the stability issues for a class of discrete-time stochastic neural networks with mixed time delays and impulsive effects. By constructing a new Lyapunov–Krasovskii functional and combining with the linear matrix inequality (LMI) approach, a novel set of sufficient conditions are derived to ensure the global asymptotic stability of the equilibrium point for the addressed discrete-time neural networks. Then the result is extended to address the problem of robust stability of uncertain discrete-time stochastic neural networks with impulsive effects. One important feature in this paper is that the stability of the equilibrium point is proved under mild conditions on the activation functions, and it is not required to be differentiable or strictly monotonic. In addition, two numerical examples are provided to show the effectiveness of the proposed method, while being less conservative.

scholarly journals Synchronization of Discrete-Time Stochastic Neural Networks with Random Delay

2011 ◽  
Vol 2011 ◽  
pp. 1-20 ◽  
Author(s):  
Haibo Bao ◽  
Jinde Cao
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Stochastic Neural Networks ◽  
Time Varying Delay ◽  
Random Delays ◽  
Random Fashion ◽  
Analysis Technique

By using a Lyapunov-Krasovskii functional method and the stochastic analysis technique, we investigate the problem of synchronization for discrete-time stochastic neural networks (DSNNs) with random delays. A control law is designed, and sufficient conditions are established that guarantee the synchronization of two identical DSNNs with random delays. Compared with the previous works, the time delay is assumed to be existent in a random fashion. The stochastic disturbances are described in terms of a Brownian motion and the time-varying delay is characterized by introducing a Bernoulli stochastic variable. Two examples are given to illustrate the effectiveness of the proposed results. The main contribution of this paper is that the obtained results are dependent on not only the bound but also the distribution probability of the time delay. Moreover, our results provide a larger allowance variation range of the delay, and are less conservative than the traditional delay-independent ones.

scholarly journals Finite-Time Synchronization of Markovian Jumping Complex Networks with Non-Identical Nodes and Impulsive Effects

Entropy ◽  
2019 ◽  
Vol 21 (8) ◽  
pp. 779
Author(s):  
Tao Chen ◽  
Shiguo Peng ◽  
Zhenhua Zhang
Keyword(s):  
Complex Networks ◽  
Finite Time ◽  
Time Synchronization ◽  
Sufficient Conditions ◽  
Impulsive Effects ◽  
Markovian Jumping ◽  
Complex Dynamic Systems ◽  
Synchronization Problem ◽  
Analysis Technique ◽  
Lyapunov Function Method

In this paper, we investigate the finite-time synchronization problem for a class of Markovian jumping complex networks (MJCNs) with non-identical nodes and impulsive effects. Sufficient conditions for the MJCNs are presented based on an M-matrix technique, Lyapunov function method, stochastic analysis technique, and suitable comparison systems to guarantee finite-time synchronization. At last, numerical examples are exploited to illustrate our theoretical results, and they testify the effectiveness of our results for complex dynamic systems.

Observer-based control for a singular Markovian jumping system

2017 ◽  
Vol 34 (1) ◽  
pp. 33-52
Author(s):  
Ching-Min Lee
Keyword(s):  
Control Problem ◽  
Control Systems ◽  
Discrete Time ◽  
Networked Control Systems ◽  
Sufficient Conditions ◽  
Networked Control ◽  
Markovian Jumping ◽  
Content Type ◽  
Robot Systems ◽  
Necessary And Sufficient

Purpose For most practical control system problems, the state variables of a system are not often available or measureable due to technical or economical constraints. In these cases, an observer-based controller design problem, which is involved with using the available information on inputs and outputs to reconstruct the unmeasured states, is desirable, and it has been wide investigated in many practical applications. However, the investigation on a discrete-time singular Markovian jumping system is few so far. This paper aims to consider an observer-based control problem for a discrete-time singular Markovian jumping system and provides a set of easy-used conditions to the proposed control law. Design/methodology/approach According to the connotation of the separation principle extended from linear systems, a mode-dependent observer and a state-feedback controller is designed and carried out independently via two sets of derived necessary and sufficient conditions in terms of linear matrix inequalities (LMIs). Findings A set of necessary and sufficient conditions for an admissibility analysis problem related to a discrete-time singular Markovian jumping system is derived to be a doctrinal foundation for the proposed design problems. A mode-dependent observer and a controller for such systems could be designed via two sets of strictly LMI-based synthesis conditions. Research limitations/implications The proposed method can be applied to discrete-time singular Markovian jumping systems with transition probability pij > 0 rather than the ones with pii = 0. Practical implications The formulated problem and proposed methods have extensive applications in various fields such as power systems, electrical circuits, robot systems, chemical systems, networked control systems and interconnected large-scale systems. Take robotic networked control systems for example. It is recognized that the variance phenomena derived from network transmission, such as packets dropout, loss and disorder, are suitable for modeling as a system with Markovian jumping modes, while the dynamics of the robot systems can be described by singular systems. In addition, the packets dropout or loss might result in unreliable transmission signals which motivates an observer-based control problem. Originality/value Both of the resultant conditions of analysis and synthesis problems for a discrete-time singular Markovian jumping system are necessary and sufficient, and are formed in strict LMIs, which can be used and implemented easily via MATLAB toolbox.

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