SYNCHRONIZATION OF TAKAGI–SUGENO FUZZY STOCHASTIC DELAYED COMPLEX NETWORKS WITH HYBRID COUPLING

2009 ◽  
Vol 23 (20n21) ◽  
pp. 2429-2447 ◽  
Author(s):  
YANG TANG ◽  
JIAN-AN FANG
Keyword(s):  
Complex Networks ◽  
Sufficient Conditions ◽  
Distributed Delay ◽  
Stochastic Perturbation ◽  
Fuzzy Model ◽  
Computationally Efficient ◽  
Stochastic Disturbances ◽  
Hybrid Coupling ◽  
Delay Dependent ◽  
Takagi Sugeno

In this paper, we propose and investigate a general model of fuzzy complex networks described by the Takagi–Sugeno (T–S) fuzzy model with hybrid coupling and stochastic perturbation. The hybrid coupling includes constant coupling and discrete and distributed delay coupling. By utilizing a new Lyapunov functional form, we employ the stochastic analysis techniques and Kronecker product to develop delay-dependent synchronization criteria that ensure mean-square synchronization of the addressed T–S fuzzy delayed complex networks with stochastic disturbances. These sufficient conditions are computationally efficient, as it can be solved numerically by the LMI toolbox in Matlab. A numerical example is provided to demonstrate the effectiveness and the applicability of the proposed method.

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 Global Synchronization of Delayed Complex Networks with Hybrid Coupling, Control Design of Actuator Saturation, and Stochastic Disturbances with Randomly Occurring Nonlinearities

2019 ◽  
Vol 2019 ◽  
pp. 1-13
Author(s):  
M. Syed Ali ◽  
M. Usha ◽  
S. Saravanan ◽  
Quanxin Zhu
Keyword(s):  
Complex Networks ◽  
Actuator Saturation ◽  
Sufficient Conditions ◽  
Distributed Delay ◽  
Control Design ◽  
Linear Matrix ◽  
Global Synchronization ◽  
Hybrid Coupling ◽  
New Type ◽  
Synchronization Scheme

In this paper, we propose and study a global synchronization of delayed complex networks with hybrid coupling, which is composed of constant coupling, discrete-delay coupling, and unbounded distributed-delay coupling, and its actuator saturation control design is then further investigated. Several effective sufficient conditions of global synchronization are attained based on the Lyapunov function and a linear matrix inequality (LMI), which can be easily computed by the interior-point method. In addition, we established the control design of actuator saturation of the addressed stochastic delayed complex networks. More relaxed conditions by employing the new type of augmented matrices by using multitude Kronecker product terms can be handled, which can be introduced. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed synchronization scheme.

Fuzzy observer–based disturbance rejection control for nonlinear fractional-order systems with time-varying delay

2021 ◽  
pp. 107754632110069
Author(s):  
Parvin Mahmoudabadi ◽  
Mahsan Tavakoli-Kakhki
Keyword(s):  
Fractional Order ◽  
Disturbance Rejection ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Delayed Systems ◽  
Fuzzy Observer ◽  
Time Varying Delay ◽  
Takagi Sugeno

In this article, a Takagi–Sugeno fuzzy model is applied to deal with the problem of observer-based control design for nonlinear time-delayed systems with fractional-order [Formula: see text]. By applying the Lyapunov–Krasovskii method, a fuzzy observer–based controller is established to stabilize the time-delayed fractional-order Takagi–Sugeno fuzzy model. Also, the problem of disturbance rejection for the addressed systems is studied via the state-feedback method in the form of a parallel distributed compensation approach. Furthermore, sufficient conditions for the existence of state-feedback gains and observer gains are achieved in the terms of linear matrix inequalities. Finally, two numerical examples are simulated for the validation of the presented methods.

scholarly journals Further results on robust fuzzy dynamic systems with LMI D-stability constraints

2014 ◽  
Vol 24 (4) ◽  
pp. 785-794 ◽  
Author(s):  
Wudhichai Assawinchaichote
Keyword(s):  
Dynamic Systems ◽  
Fuzzy Controller ◽  
Sufficient Conditions ◽  
Fuzzy Model ◽  
Local System ◽  
Linear Matrix ◽  
Fuzzy Modelling ◽  
Ts Fuzzy Model ◽  
Input Noise ◽  
Takagi Sugeno

Abstract This paper examines the problem of designing a robust H∞ fuzzy controller with D-stability constraints for a class of nonlinear dynamic systems which is described by a Takagi-Sugeno (TS) fuzzy model. Fuzzy modelling is a multi-model approach in which simple sub-models are combined to determine the global behavior of the system. Based on a linear matrix inequality (LMI) approach, we develop a robust H∞ fuzzy controller that guarantees (i) the L2-gain of the mapping from the exogenous input noise to the regulated output to be less than some prescribed value, and (ii) the closed-loop poles of each local system to be within a specified stability region. Sufficient conditions for the controller are given in terms of LMIs. Finally, to show the effectiveness of the designed approach, an example is provided to illustrate the use of the proposed methodology.

A DELAY-DEPENDENT APPROACH TO ROBUST TAKAGI–SUGENO FUZZY CONTROL OF UNCERTAIN RECURRENT NEURAL NETWORKS WITH MIXED INTERVAL TIME-VARYING DELAYS

2011 ◽  
Vol 20 (08) ◽  
pp. 1571-1589 ◽  
Author(s):  
K. H. TSENG ◽  
J. S. H. TSAI ◽  
C. Y. LU
Keyword(s):  
Fuzzy Control ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Upper And Lower Bounds ◽  
Linear Matrix ◽  
Uncertain Parameters ◽  
Time Varying ◽  
Interval Time ◽  
Delay Dependent ◽  
Takagi Sugeno

This paper deals with the problem of globally delay-dependent robust stabilization for Takagi–Sugeno (T–S) fuzzy neural network with time delays and uncertain parameters. The time delays comprise discrete and distributed interval time-varying delays and the uncertain parameters are norm-bounded. Based on Lyapunov–Krasovskii functional approach and linear matrix inequality technique, delay-dependent sufficient conditions are derived for ensuring the exponential stability for the closed-loop fuzzy control system. An important feature of the result is that all the stability conditions are dependent on the upper and lower bounds of the delays, which is made possible by using the proposed techniques for achieving delay dependence. Another feature of the results lies in that involves fewer matrix variables. Two illustrative examples are exploited in order to illustrate the effectiveness of the proposed design methods.

DELAYED FUZZY CONTROLLER DESIGN FOR HYPERCHAOS WITH APPLICATION TO HYPERCHAOTIC CHEN'S SYSTEM

2007 ◽  
Vol 18 (07) ◽  
pp. 1095-1105 ◽  
Author(s):  
XINGWEN LIU ◽  
XIN GAO
Keyword(s):  
Fuzzy Controller ◽  
Controller Design ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Delayed State Feedback ◽  
Delay Dependent ◽  
Takagi Sugeno ◽  
Compensation Design ◽  
Hyperchaotic Systems ◽  
Control Criterion

Studied in this paper is the control problem of hyperchaotic systems. By combining Takagi–Sugeno (T–S) fuzzy model with parallel distributed compensation design technique, we propose a delay-dependent control criterion via pure delayed state feedback. Because the result is expressed in terms of linear matrix inequalities (LMIs), it is quite convenient to check in practice. Based on this criterion, a procedure is provided for designing fuzzy controller for such systems. This method is a universal one for controlling continuous hyperchaotic systems. As illustrated by its application to hyperchaotic Chen's system, the controller design is quite effective.

scholarly journals Mean Square Synchronization of Stochastic Nonlinear Delayed Coupled Complex Networks

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Chengrong Xie ◽  
Yuhua Xu ◽  
Dongbing Tong
Keyword(s):  
Complex Networks ◽  
Numerical Simulations ◽  
Invariance Principle ◽  
Sufficient Conditions ◽  
Stochastic Perturbation ◽  
Mean Square ◽  
Topology Identification ◽  
And Topology ◽  
Adaptive Laws ◽  
Weiner Process

We investigate the problem of adaptive mean square synchronization for nonlinear delayed coupled complex networks with stochastic perturbation. Based on the LaSalle invariance principle and the properties of the Weiner process, the controller and adaptive laws are designed to ensure achieving stochastic synchronization and topology identification of complex networks. Sufficient conditions are given to ensure the complex networks to be mean square synchronization. Furthermore, numerical simulations are also given to demonstrate the effectiveness of the proposed scheme.

scholarly journals Model reduction design for continuous systems with finite frequency specifications

2021 ◽  
Vol 11 (5) ◽  
pp. 3956
Author(s):  
Miloud Koumir ◽  
Abderrahim El-Amrani ◽  
Ismail Boumhidi
Keyword(s):  
Model Reduction ◽  
Sufficient Conditions ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Continuous Systems ◽  
Asymptotically Stable ◽  
Matrix Inequalities ◽  
Finite Frequency ◽  
Error System ◽  
Takagi Sugeno

<p>This paper is concerned with the problem of model reduction design for continuous systems in Takagi-Sugeno fuzzy model. Through the defined FF H∞ gain performance, sufficient conditions are derived to design model reduction and to assure the fuzzy error system to be asymptotically stable with a FF H∞ gain performance index. The explicit conditions of fuzzy model reduction are developed by solving linear matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.</p>

H∞ Filtering for Nonlinear Systems with Time Delays via Takagi-Sugeno Fuzzy Model

2012 ◽  
Vol 557-559 ◽  
pp. 2033-2038
Author(s):  
Jun Sheng Ren ◽  
Xian Ku Zhang
Keyword(s):  
Time Delays ◽  
Controller Design ◽  
Filter Design ◽  
Estimation Error ◽  
Fuzzy Model ◽  
Error System ◽  
Delay Dependent ◽  
S Model ◽  
Takagi Sugeno ◽  
Filtering Problem

State estimation is an important topic in controller design. H∞filtering problem is discussed for fuzzy dynamical systems with time delays by using Takagi-Sugeno (T-S) model. Fuzzy H∞filter is obtained such that the filtering error system is stable and guarantees a prescribed estimation error level. Delay-dependent Lyapunov functional approach is employed to lower the conservativeness of the filter design. Therefore, the results of fuzzy H∞filter are delay-dependent. An example is given to illustrate the proposed results.

scholarly journals Study on Bifurcation Analysis and Takagi-Sugeno Fuzzy Sampled-Data Stabilization of PMSM Systems

2021 ◽  
Author(s):  
R Vadivel ◽  
Sabarathinam Srinivasan ◽  
Yongbao Wu ◽  
NALLAPPAN GUNASEKARAN
Keyword(s):  
Fuzzy System ◽  
Permanent Magnet Synchronous Motor ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Sampled Data ◽  
Matlab Toolbox ◽  
New Class ◽  
Data Control ◽  
Delay Dependent ◽  
Takagi Sugeno

The bifurcation, stability and stabilization analysis of permanent magnet synchronous motor (PMSM) systems are investigated in this paper. To begin, a new class of delay-dependent sufficient conditions is suggested with respect to the information of the membership function, a relevant Lyapunov-Krasovskii functional (LKF), and the overall information connected with the real sampling pattern, so that the fuzzy system is ensured to be stable with a weighted dissipativity efficiency. Second, sampled-data control is intended to stabilize the Takagi-Sugeno (T-S) fuzzy system with specified integral inequalities based on the obtained results. The required conditions are stated in terms of the feasibility of linear matrix inequalities (LMIs) under the dissipativity output index, and can readily be verified by MATLAB toolbox. Finally, verification examples are contributed to demonstrated the efficacy of the techniques established in this paper.

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