Linear matrix inequality-based novel stability criteria of the primal-dual algorithm with heterogeneous communication delays

2010 ◽  
Vol 4 (3) ◽  
pp. 461-471 ◽  
Author(s):  
S. Guo ◽  
X. Liao ◽  
D. Liu ◽  
C. Dang
Keyword(s):  
Linear Matrix Inequality ◽  
Linear Matrix ◽  
Communication Delays ◽  
Matrix Inequality ◽  
Stability Criteria ◽  
Dual Algorithm ◽  
Primal Dual

Novel Approach to Robust Stability Criteria of Uncertain System with Time-Varying Delay

2013 ◽  
Vol 631-632 ◽  
pp. 1189-1194
Author(s):  
Chao Deng ◽  
Zhao Di Xu ◽  
Yu Bai ◽  
Xin Yuan Wang
Keyword(s):  
Linear Matrix Inequality ◽  
Robust Stability ◽  
Uncertain System ◽  
Linear Matrix ◽  
Convexity Property ◽  
Time Varying ◽  
Matrix Inequality ◽  
Stability Criteria ◽  
Time Varying Delay ◽  
Varying Delay

This paper considers the robust stability criteria of uncertain system with time-varying delay. Firstly, by exploiting a new Lyapunov function that optimizes the segment of time delay and using the convexity property and free-weight method of the Linear Matrix Inequality, delay-dependent stability condition can be obtained for the asymptotical stability of the nominal system. Secondly, basing on the obtained condition, the corresponding linear matrix inequality can be obtained for the uncertain system. Finally, an example is given to demostrate the effectiveness and the merit of the proposed method.

scholarly journals A Reconstruction Procedure Associated with Switching Lyapunov Function for Relaxing Stability Assurance of T-S Fuzzy Mode

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Yau-Tarng Juang ◽  
Chih-Peng Huang ◽  
Chung-Lin Yan
Keyword(s):  
Lyapunov Function ◽  
Linear Matrix Inequality ◽  
Fuzzy Model ◽  
Alternative Form ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
State Variables ◽  
Stability Criteria ◽  
Quadratic Lyapunov Function ◽  
Reconstruction Procedure

This paper proposes a novel reconstruction procedure to lessen the conservatism of stability assurance of T-S Fuzzy Mode. By dividing the state variables into some bounded regions, the considered T-S fuzzy model can be first transferred to an alternative form via a reconstructing procedure. Thus, we can attain some relaxing stability criteria based on the switching quadratic Lyapunov function (SQLF) method. Notably, these proposed conditions are explicitly formulated by linear matrix inequality (LMI) form and can handily be evaluated by current software tools. Finally some illustrative examples are given to experimentally demonstrate the validity and merit of the proposed method.

scholarly journals Pinning Synchronization of Delayed Neural Networks with Nonlinear Inner-Coupling

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Yangling Wang ◽  
Jinde Cao
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Stability Criteria ◽  
Delayed Neural Networks ◽  
Delay Dependent

Without assuming the symmetry and irreducibility of the outer-coupling weight configuration matrices, we investigate the pinning synchronization of delayed neural networks with nonlinear inner-coupling. Some delay-dependent controlled stability criteria in terms of linear matrix inequality (LMI) are obtained. An example is presented to show the application of the criteria obtained in this paper.

scholarly journals Synthesis of Polynomial Fuzzy Model-Based Designs with Synchronization and Secure Communications for Chaos Systems with H∞ Performance

Processes ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 2088
Author(s):  
Gwo-Ruey Yu ◽  
Yong-Dong Chang ◽  
Chih-Heng Chang
Keyword(s):  
Lyapunov Function ◽  
Linear Matrix Inequality ◽  
Numerical Simulations ◽  
Fuzzy System ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Secure Communications ◽  
Matrix Inequality ◽  
Stability Criteria ◽  
Fuzzy Compensator

This paper presents the sum of squares (SOS)-based fuzzy control with H∞ performance for a synchronized chaos system and secure communications. To diminish the influence of the extrinsic perturbation, SOS-based stability criteria of the polynomial fuzzy system are derived by using the polynomial Lyapunov function. The perturbation decreasing achievement is indexed in a H∞ criterion. The submitted SOS-based stability criteria are more relaxed than the existing linear matrix inequality (LMI)-based stability criteria. The cryptography scheme based on an n-shift cipher is combined with synchronization for secure communications. Finally, numerical simulations illustrate the perturbation decay accomplishment of the submitted polynomial fuzzy compensator.

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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