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.

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 On Stability Analysis for Generalized Neural Networks with Time-Varying Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
M. J. Park ◽  
O. M. Kwon ◽  
E. J. Cha
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Asymptotic Stability ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Numerical Examples ◽  
Generalized Neural Networks

This paper deals with the problem of stability analysis for generalized neural networks with time-varying delays. With a suitable Lyapunov-Krasovskii functional (LKF) and Wirtinger-based integral inequality, sufficient conditions for guaranteeing the asymptotic stability of the concerned networks are derived in terms of linear matrix inequalities (LMIs). By applying the proposed methods to two numerical examples which have been utilized in many works for checking the conservatism of stability criteria, it is shown that the obtained results are significantly improved comparing with the previous ones published in other literature.

Robust Finite-Time Passivity for Discrete-Time Genetic Regulatory Networks with Markovian Jumping Parameters

2016 ◽  
Vol 71 (4) ◽  
pp. 289-304 ◽  
Author(s):  
R. Sakthivel ◽  
M. Sathishkumar ◽  
B. Kaviarasan ◽  
S. Marshal Anthoni
Keyword(s):  
Discrete Time ◽  
Finite Time ◽  
Regulatory Networks ◽  
Sufficient Conditions ◽  
Schur Complement ◽  
Genetic Regulatory Networks ◽  
Linear Matrix ◽  
Time Interval ◽  
Markovian Jumping Parameters ◽  
Markovian Jumping

AbstractThis article addresses the issue of robust finite-time passivity for a class of uncertain discrete-time genetic regulatory networks (GRNs) with time-varying delays and Markovian jumping parameters. By constructing a proper Lyapunov–Krasovskii functional involving the lower and upper bounds of time delays, a new set of sufficient conditions is obtained in terms of linear matrix inequalities (LMIs), which guarantees the finite-time boundedness and finite-time passivity of the addressed GRNs for all admissible uncertainties and satisfies the given passive performance index. More precisely, the conditions are obtained with respect to the finite-time interval, while the exogenous disturbances are unknown but energy bounded. Furthermore, the Schur complement together with reciprocally convex optimisation approach is used to simplify the derivation in the main results. Finally, three numerical examples are provided to illustrate the validity of the obtained 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 Finite-Time H ∞ State Estimation for Markovian Jump Neural Networks with Time-Varying Delays via an Extended Wirtinger’s Integral Inequality

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Saravanan Shanmugam ◽  
M. Syed Ali ◽  
R. Vadivel ◽  
Gyu M. Lee
Keyword(s):  
Neural Networks ◽  
Finite Time ◽  
Transition Probabilities ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Markovian Jump ◽  
Markovian Jumping ◽  
Double Inequality ◽  
Markovian Jump Neural Networks

This study investigates the finite-time boundedness for Markovian jump neural networks (MJNNs) with time-varying delays. An MJNN consists of a limited number of jumping modes wherein it can jump starting with one mode then onto the next by following a Markovian process with known transition probabilities. By constructing new Lyapunov–Krasovskii functional (LKF) candidates, extended Wirtinger’s, and Wirtinger’s double inequality with multiple integral terms and using activation function conditions, several sufficient conditions for Markovian jumping neural networks are derived. Furthermore, delay-dependent adequate conditions on guaranteeing the closed-loop system which are stochastically finite-time bounded (SFTB) with the prescribed H ∞ performance level are proposed. Linear matrix inequalities are utilized to obtain analysis results. The purpose is to obtain less conservative conditions on finite-time H ∞ performance for Markovian jump neural networks with time-varying delay. Eventually, simulation examples are provided to illustrate the validity of the addressed method.

scholarly journals NonfragileH∞Control for Stochastic Systems with Markovian Jumping Parameters and Random Packet Losses

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Jing Wang ◽  
Ke Zhang
Keyword(s):  
Closed Loop ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Markovian Jumping Parameters ◽  
Matrix Inequalities ◽  
Closed Loop System ◽  
Packet Losses ◽  
Markovian Jumping ◽  
Physical Plant

This paper is concerned with the nonfragileH∞control problem for stochastic systems with Markovian jumping parameters and random packet losses. The communication between the physical plant and controller is assumed to be imperfect, where random packet losses phenomenon occurs in a random way. Such a phenomenon is represented by a stochastic variable satisfying the Bernoulli distribution. The purpose is to design a nonfragile controller such that the resulting closed-loop system is stochastically mean square stable with a guaranteedH∞performance levelγ. By using the Lyapunov function approach, some sufficient conditions for the solvability of the previous problem are proposed in terms of linear matrix inequalities (LMIs), and a corresponding explicit parametrization of the desired controller is given. Finally, an example illustrating the effectiveness of the proposed approach is presented.

scholarly journals Robust Stability of Complex-Valued Stochastic Neural Networks with Time-Varying Delays and Parameter Uncertainties

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 742 ◽  
Author(s):  
Pharunyou Chanthorn ◽  
Grienggrai Rajchakit ◽  
Jenjira Thipcha ◽  
Chanikan Emharuethai ◽  
Ramalingam Sriraman ◽  
...  
Keyword(s):  
Neural Networks ◽  
Robust Stability ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Equivalent Representation ◽  
Stochastic Effects ◽  
Complex Valued

In practical applications, stochastic effects are normally viewed as the major sources that lead to the system’s unwilling behaviours when modelling real neural systems. As such, the research on network models with stochastic effects is significant. In view of this, in this paper, we analyse the issue of robust stability for a class of uncertain complex-valued stochastic neural networks (UCVSNNs) with time-varying delays. Based on the real-imaginary separate-type activation function, the original UCVSNN model is analysed using an equivalent representation consisting of two real-valued neural networks. By constructing the proper Lyapunov–Krasovskii functional and applying Jensen’s inequality, a number of sufficient conditions can be derived by utilizing It o ^ ’s formula, the homeomorphism principle, the linear matrix inequality, and other analytic techniques. As a result, new sufficient conditions to ensure robust, globally asymptotic stability in the mean square for the considered UCVSNN models are derived. Numerical simulations are presented to illustrate the merit of the obtained results.

H ∞ Guaranteed Cost Filtering for Uncertain Discrete-Time Switched Systems With Multiple Time-Varying Delays

2010 ◽  
Vol 133 (1) ◽  
Author(s):  
Haibin Sun ◽  
Guangdeng Zong ◽  
Linlin Hou
Keyword(s):  
Discrete Time ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Multiple Time ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Guaranteed Cost ◽  
The Cost

This paper deals with the problem of H∞ guaranteed cost filtering for uncertain discrete-time switched systems with multiple time-varying delays. The switched system under consideration is subject to time-varying norm-bounded parameter uncertainties in all the system matrices. The aim is to design a filter, which guarantees the asymptotical stability of the error system with prescribed disturbance attenuation for all admissible uncertainties and the cost function value is not more than a specified upper bound. By resorting to a switched Lyapunov function, some delay-dependent sufficient conditions are presented in terms of linear matrix inequalities. A numerical example is provided to demonstrate the effectiveness of the proposed algorithms.

scholarly journals Synchronization Analysis for Stochastic T-S Fuzzy Complex Networks with Markovian Jumping Parameters and Mixed Time-Varying Delays via Impulsive Control

2020 ◽  
Vol 2020 ◽  
pp. 1-27 ◽  
Author(s):  
M. Syed Ali ◽  
M. Usha ◽  
Quanxin Zhu ◽  
Saravanan Shanmugam
Keyword(s):  
Complex Networks ◽  
Impulsive Control ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Time Varying ◽  
Markovian Jumping Parameters ◽  
Markovian Jumping ◽  
Stochastic Complex Networks ◽  
Delay Dependent ◽  
Takagi Sugeno

In this paper, we propose and explore the synchronization examination for fuzzy stochastic complex networks’ Markovian jumping parameters portrayed by Takagi-Sugeno (T-S) fuzzy model with mixed time-varying coupling delays via impulsive control. The hybrid coupling includes time-varying discrete and distributed delays. Based on appropriate Lyapunov–Krasovskii functional (LKF) approach, Newton–Leibniz formula, and Jensen’s inequality, the stochastic examination systems and Kronecker product to create delay-dependent synchronization criteria that guarantee stochastically synchronous of the proposed T-S fuzzy stochastic complex networks with mixed time-varying delays. Adequate conditions for the synchronization criteria for the frameworks are established in terms of linear matrix inequalities (LMIs). At long last, numerical examples and simulations are given to demonstrate the correctness of the hypothetical outcomes.

scholarly journals Analysis on Passivity for Uncertain Neural Networks with Time-Varying Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
O. M. Kwon ◽  
M. J. Park ◽  
Ju H. Park ◽  
S. M. Lee ◽  
E. J. Cha
Keyword(s):  
Neural Networks ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Feasible Region ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
Numerical Examples ◽  
Passivity Analysis ◽  
Uncertain Neural Networks

The problem of passivity analysis for neural networks with time-varying delays and parameter uncertainties is considered. By the consideration of newly constructed Lyapunov-Krasovskii functionals, improved sufficient conditions to guarantee the passivity of the concerned networks are proposed with the framework of linear matrix inequalities (LMIs), which can be solved easily by various efficient convex optimization algorithms. The enhancement of the feasible region of the proposed criteria is shown via two numerical examples by the comparison of maximum allowable delay bounds.

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