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 Robust Adaptive Exponential Synchronization of Two Different Stochastic Perturbed Chaotic Systems with Structural Perturbations

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
A. Soup Tewa Kammogne ◽  
H. B. Fotsin
Keyword(s):  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Exponential Synchronization ◽  
Analysis Tool ◽  
Mean Square ◽  
Stochastic Disturbances ◽  
Parameter Uncertainties ◽  
Structural Perturbations ◽  
Robust Adaptive

The robust adaptive exponential synchronization problem of stochastic chaotic systems with structural perturbations is investigated in mean square. The stochastic disturbances are assumed to be Brownian motions that act on the slave system and the norm-bounded uncertainties exist in all parameters after decoupling. The stochastic disturbances could reflect more realistic dynamical behaviors of the coupled chaotic system presented within a noisy environment. By using a combination of the Lyapunov functional method, the robust analysis tool, the stochastic analysis techniques, and adaptive control laws, we derive several sufficient conditions that ensure the coupled chaotic systems to be robustly exponentially synchronized in the mean square for all admissible parameter uncertainties. This approach cannot only make the outputs of both master and slave systems reach H∞ synchronization with the passage of time between both systems but also attenuate the effects of the perturbation on the overall error system to a prescribed level. The main results are shown to be general enough to cover many existing ones reported in the literature.

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 An Extended Analysis on Robust Dissipativity of Uncertain Stochastic Generalized Neural Networks with Markovian Jumping Parameters

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1035
Author(s):  
Usa Humphries ◽  
Grienggrai Rajchakit ◽  
Ramalingam Sriraman ◽  
Pramet Kaewmesri ◽  
Pharunyou Chanthorn ◽  
...  
Keyword(s):  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Markovian Jumping Parameters ◽  
Stochastic Disturbances ◽  
Parameter Uncertainties ◽  
Markovian Jumping ◽  
Generalized Neural Networks ◽  
Extended Analysis ◽  
Feasible Solutions

The main focus of this research is on a comprehensive analysis of robust dissipativity issues pertaining to a class of uncertain stochastic generalized neural network (USGNN) models in the presence of time-varying delays and Markovian jumping parameters (MJPs). In real-world environments, most practical systems are subject to uncertainties. As a result, we take the norm-bounded parameter uncertainties, as well as stochastic disturbances into consideration in our study. To address the task, we formulate the appropriate Lyapunov–Krasovskii functional (LKF), and through the use of effective integral inequalities, simplified linear matrix inequality (LMI) based sufficient conditions are derived. We validate the feasible solutions through numerical examples using MATLAB software. The simulation results are analyzed and discussed, which positively indicate the feasibility and effectiveness of the obtained theoretical findings.

Robust H2 Output Feedback Controller Design for Damping Power System Oscillations

2017 ◽  
Vol 6 (10) ◽  
pp. 8
Author(s):  
Kho Hie Kwee ◽  
Hardiansyah .
Keyword(s):  
Power System ◽  
Output Feedback ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Feedback Controller ◽  
Linear Matrix ◽  
Parameter Uncertainties ◽  
Worst Case ◽  
Output Feedback Controller ◽  
Power System Oscillations

This paper addresses the design problem of robust H2 output feedback controller design for damping power system oscillations. Sufficient conditions for the existence of output feedback controllers with norm-bounded parameter uncertainties are given in terms of linear matrix inequalities (LMIs). Furthermore, a convex optimization problem with LMI constraints is formulated to design the output feedback controller which minimizes an upper bound on the worst-case H2 norm for a range of admissible plant perturbations. The technique is illustrated with applications to the design of stabilizer for a single-machine infinite-bus (SMIB) power system. The LMI based control ensures adequate damping for widely varying system operating.

Robust stability analysis for delayed Cohen-Grossberg-type bidirectional associative memory neural networks with norm-bounded uncertainties

2009 ◽  
Vol 223 (5) ◽  
pp. 693-707
Author(s):  
Y Wang ◽  
P Hu
Keyword(s):  
Neural Networks ◽  
Associative Memory ◽  
Robust Stability ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Bidirectional Associative Memory ◽  
Parameter Uncertainties ◽  
Robust Stability Analysis ◽  
Global Robust Stability ◽  
Bounded Uncertainties

In this paper, the problem of global robust stability is discussed for uncertain Cohen-Grossberg-type (CG-type) bidirectional associative memory (BAM) neural networks (NNs) with delays. The parameter uncertainties are supposed to be norm bounded. The sufficient conditions for global robust stability are derived by employing a Lyapunov-Krasovskii functional. Based on these, the conditions ensuring global asymptotic stability without parameter uncertainties are established. All conditions are expressed in terms of linear matrix inequalities (LMIs). In addition, two examples are provided to illustrate the effectiveness of the results obtained.

scholarly journals Nonfragile H∞ Filter Design for Nonlinear Continuous-Time System with Interval Time-Varying Delay

2018 ◽  
Vol 2018 ◽  
pp. 1-17
Author(s):  
Zhongda Lu ◽  
Guoliang Zhang ◽  
Yi Sun ◽  
Jie Sun ◽  
Fangming Jin ◽  
...  
Keyword(s):  
Continuous Time ◽  
Filter Design ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Decoupling Method ◽  
Interval Time ◽  
Time Varying Delay ◽  
Error System ◽  
Delay Dependent

This paper investigates nonfragile H∞ filter design for a class of continuous-time delayed Takagi-Sugeno (T-S) fuzzy systems with interval time-varying delays. Filter parameters occur multiplicative gain variations according to the filter’s implementation, to handle this variations, a nonfragile H∞ filter is presented and a novel filtering error system is established. The nonfragile H∞ filter guarantees the filtering error system to be asymptotically stable and satisfies given H∞ performance index. By constructing a novel Lyapunov-Krasovskii function and using the linear matrix inequality (LMI), delay-dependent conditions are exploited to derive sufficient conditions for nonfragile designing H∞ filter. Using new matrix decoupling method to reduce the computational complexity, the filter parameters can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, numerical examples are given to show the effectiveness of the proposed method.

scholarly journals Robust Synchronization Criterion for Coupled Stochastic Discrete-Time Neural Networks with Interval Time-Varying Delays, Leakage Delay, and Parameter Uncertainties

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
M. J. Park ◽  
O. M. Kwon ◽  
Ju H. Park ◽  
S. M. Lee ◽  
E. J. Cha
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Leakage Term ◽  
Interval Time ◽  
Robust Synchronization ◽  
Delay Dependent ◽  
Finsler’S Lemma

The purpose of this paper is to investigate a delay-dependent robust synchronization analysis for coupled stochastic discrete-time neural networks with interval time-varying delays in networks coupling, a time delay in leakage term, and parameter uncertainties. Based on the Lyapunov method, a new delay-dependent criterion for the synchronization of the networks is derived in terms of linear matrix inequalities (LMIs) by constructing a suitable Lyapunov-Krasovskii’s functional and utilizing Finsler’s lemma without free-weighting matrices. Two numerical examples are given to illustrate the effectiveness of the proposed methods.

scholarly journals Stability and Stabilization of Continuous-Time Markovian Jump Singular Systems with Partly Known Transition Probabilities

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Jumei Wei ◽  
Rui Ma
Keyword(s):  
Continuous Time ◽  
Controller Design ◽  
Partial Information ◽  
Transition Probabilities ◽  
Singular Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Markovian Jump ◽  
Stability And Stabilization ◽  
The Stability

This paper investigates the problem of the stability and stabilization of continuous-time Markovian jump singular systems with partial information on transition probabilities. A new stability criterion which is necessary and sufficient is obtained for these systems. Furthermore, sufficient conditions for the state feedback controller design are derived in terms of linear matrix inequalities. Finally, numerical examples are given to illustrate the effectiveness of the proposed methods.

DELAY-DEPENDENT ROBUST EXPONENTIAL STABILITY FOR UNCERTAIN RECURRENT NEURAL NETWORKS WITH TIME-VARYING DELAYS

2007 ◽  
Vol 17 (03) ◽  
pp. 207-218 ◽  
Author(s):  
BAOYONG ZHANG ◽  
SHENGYUAN XU ◽  
YONGMIN LI
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Recurrent Neural Networks ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Robust Exponential Stability ◽  
Neuron Activation ◽  
Exponentially Stable

This paper considers the problem of robust exponential stability for a class of recurrent neural networks with time-varying delays and parameter uncertainties. The time delays are not necessarily differentiable and the uncertainties are assumed to be time-varying but norm-bounded. Sufficient conditions, which guarantee that the concerned uncertain delayed neural network is robustly, globally, exponentially stable for all admissible parameter uncertainties, are obtained under a weak assumption on the neuron activation functions. These conditions are dependent on the size of the time delay and expressed in terms of linear matrix inequalities. Numerical examples are provided to demonstrate the effectiveness and less conservatism of the proposed stability results.

scholarly journals Global Exponential Stability of Learning-Based Fuzzy Networks on Time Scales

2015 ◽  
Vol 2015 ◽  
pp. 1-15
Author(s):  
Juan Chen ◽  
Zhenkun Huang ◽  
Jinxiang Cai
Keyword(s):  
Exponential Stability ◽  
Time Scales ◽  
Continuous Time ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Fuzzy Neural Networks ◽  
New Learning ◽  
Fuzzy Neural ◽  
Lyapunov Functional Method

We investigate a class of fuzzy neural networks with Hebbian-type unsupervised learning on time scales. By using Lyapunov functional method, some new sufficient conditions are derived to ensure learning dynamics and exponential stability of fuzzy networks on time scales. Our results are general and can include continuous-time learning-based fuzzy networks and corresponding discrete-time analogues. Moreover, our results reveal some new learning behavior of fuzzy synapses on time scales which are seldom discussed in the literature.

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