scholarly journals Pinning Synchronization for Complex Networks with Interval Coupling Delay by Variable Subintervals Method and Finsler’s Lemma

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Dawei Gong ◽  
Frank L. Lewis ◽  
Liping Wang ◽  
Dong Dai ◽  
Shuang Zhang
Keyword(s):  
Linear Matrix Inequality ◽  
Complex Networks ◽  
Pinning Control ◽  
Stability Theorem ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Coupling Delay ◽  
Leibniz Formula ◽  
The Stability ◽  
Finsler’S Lemma

The pinning synchronous problem for complex networks with interval delays is studied in this paper. First, by using an inequality which is introduced from Newton-Leibniz formula, a new synchronization criterion is derived. Second, combining Finsler’s Lemma with homogenous matrix, convergent linear matrix inequality (LMI) relaxations for synchronization analysis are proposed with matrix-valued coefficients. Third, a new variable subintervals method is applied to expand the obtained results. Different from previous results, the interval delays are divided into some subdelays, which can introduce more free weighting matrices. Fourth, the results are shown as LMI, which can be easily analyzed or tested. Finally, the stability of the networks is proved via Lyapunov’s stability theorem, and the simulation of the trajectory claims the practicality of the proposed pinning control.

scholarly journals Analysis of Robust Stability for a Class of Stochastic Systems via Output Feedback: The LMI Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Xin-rong Cong ◽  
Long-suo Li
Keyword(s):  
Linear Matrix Inequality ◽  
Robust Stability ◽  
Output Feedback ◽  
Stochastic Systems ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Convex Optimization Problem ◽  
Control Laws ◽  
The Stability ◽  
And Control

This paper investigates the robust stability for a class of stochastic systems with both state and control inputs. The problem of the robust stability is solved via static output feedback, and we convert the problem to a constrained convex optimization problem involving linear matrix inequality (LMI). We show how the proposed linear matrix inequality framework can be used to select a quadratic Lyapunov function. The control laws can be produced by assuming the stability of the systems. We verify that all controllers can robustly stabilize the corresponding system. Further, the numerical simulation results verify the theoretical analysis results.

STABILITY ANALYSIS FOR DELAYED CELLULAR NEURAL NETWORKS BASED ON LINEAR MATRIX INEQUALITY APPROACH

2004 ◽  
Vol 14 (09) ◽  
pp. 3377-3384 ◽  
Author(s):  
XIAOFENG LIAO ◽  
KWOK-WO WONG ◽  
SHIZHONG YANG
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Linear Matrix Inequality Approach ◽  
Functional Differential ◽  
The Stability

Some sufficient conditions for the asymptotic stability of cellular neural networks with time delay are derived using the Lyapunov–Krasovskii stability theory for functional differential equations as well as the linear matrix inequality (LMI) approach. The analysis shows how some well-known results can be refined and generalized in a straightforward manner. Moreover, the stability criteria obtained are delay-independent. They are less conservative and restrictive than those reported so far in the literature, and provide a more general set of criteria for determining the stability of delayed cellular neural networks.

scholarly journals Stability of Hybrid Stochastic Systems with Time-Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Pu Xing-cheng ◽  
Yuan Wei
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Time Delay ◽  
Linear Matrix Inequality ◽  
Hybrid Systems ◽  
Stochastic Systems ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Hybrid Stochastic Systems ◽  
The Stability

This paper develops some criteria for a kind of hybrid stochastic systems with time-delay, which improve existing results on hybrid systems without considering noises. The improved results show that the presence of noise is quite involved in the stability analysis of hybrid systems. New results can be used to analyze the stability of a kind of stochastic hybrid impulsive and switching neural networks (SHISNN). Therefore, stability analysis of SHISNN can be turned into solving a linear matrix inequality (LMI).

Robust Control of Variable Pitch Wind Turbines Base on Linear Matrix Inequality

2011 ◽  
Vol 291-294 ◽  
pp. 2754-2759
Author(s):  
Lu Fang Qin ◽  
Tao Sun ◽  
Hua Feng Guo
Keyword(s):  
Robust Control ◽  
Linear Matrix Inequality ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Robust Tracking ◽  
Generation System ◽  
Calculating Method ◽  
Tracking Controller ◽  
Power Generation System ◽  
The Stability

In order to solve the problems of wind power generation system model uncertainty, we designed a robust tracking controller according to the robust control theories and the method of linear matrix inequality (LMI). For ensuring the stability and dynamic characteristics of robust, we gave the calculating method of proportion and integral gains, researched the robust control strategy with pole constraint that is based on minimal power tracking controller. The results of the simulation show the controller can realize the steady close-loop and possess good disturbance rejection and dynamic characteristic in some disturbances and uncertainties existed in system.

scholarly journals A New Robust Training Law for Dynamic Neural Networks with External Disturbance: An LMI Approach

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Choon Ki Ahn
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Exponential Stability ◽  
External Disturbance ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Input Output ◽  
Lmi Approach ◽  
Dynamic Neural Networks ◽  
Numerical Examples

A new robust training law, which is called an input/output-to-state stable training law (IOSSTL), is proposed for dynamic neural networks with external disturbance. Based on linear matrix inequality (LMI) formulation, the IOSSTL is presented to not only guarantee exponential stability but also reduce the effect of an external disturbance. It is shown that the IOSSTL can be obtained by solving the LMI, which can be easily facilitated by using some standard numerical packages. Numerical examples are presented to demonstrate the validity of the proposed IOSSTL.

Cellular Neural Network Based on Hybrid Linear Matrix Inequality and Particle Swarm Optimization for Noise Removal of Color Image

2011 ◽  
Vol 422 ◽  
pp. 771-774
Author(s):  
Te Jen Su ◽  
Jui Chuan Cheng ◽  
Yu Jen Lin
Keyword(s):  
Neural Network ◽  
Particle Swarm Optimization ◽  
Linear Matrix Inequality ◽  
Color Image ◽  
Particle Swarm ◽  
Cellular Neural Network ◽  
Noise Removal ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Swarm Optimization

This paper presents a color image noise removal technique that employs a cellular neural network (CNN) based on hybrid linear matrix inequality (LMI) and particle swarm optimization (PSO). For designing templates of CNN, the Lyapunov stability theorem is applied to derive the criterion for the uniqueness and global asymptotic stability of the CNN’s equilibrium point. The template design is characterized as a standard LMI problem, and the parameters of templates are optimized by PSO. The input templates are obtained by employing the CNN’s property of saturation nonlinearity, which can be used to eliminate noise from arbitrary corrupted images. The demonstrated examples are compared favorably with other available methods, which illustrate the better performance of the proposed LMI-PSO-CNN methodology.

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