scholarly journals Distributed Optimization of Multiagent Systems in Directed Networks with Time-Varying Delay

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Junxiu Yan ◽  
Hui Yu
Keyword(s):  
Optimization Problem ◽  
Multiagent System ◽  
Distributed Optimization ◽  
Optimal Solution ◽  
Time Varying ◽  
Razumikhin Theorem ◽  
First Order ◽  
Time Varying Delay ◽  
Consensus Optimization ◽  
Varying Delay

This paper addresses a distributed consensus optimization problem of a first-order multiagent system with time-varying delay. A continuous-time distributed optimization algorithm is proposed. Different from most ways of solving distributed optimization problem, the Lyapunov-Razumikhin theorem is applied to the convergence analysis instead of the Lyapunov-Krasovskii functionals with LMI conditions. A sufficient condition for the control parameters is obtained to make all the agents converge to the optimal solution of the system. Finally, an example is given to validate the effectiveness of our theoretical result.

Mean-Square Exponential Stability of Stochastic Interval Cellular Neural Networks with Time-Varying Delay

2013 ◽  
Vol 760-762 ◽  
pp. 1742-1747
Author(s):  
Jin Fang Han
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Cellular Neural Networks ◽  
Time Varying ◽  
Mean Square ◽  
Razumikhin Theorem ◽  
Time Varying Delay ◽  
Mean Square Exponential Stability ◽  
The Mean ◽  
Varying Delay

This paper is concerned with the mean-square exponential stability analysis problem for a class of stochastic interval cellular neural networks with time-varying delay. By using the stochastic analysis approach, employing Lyapunov function and norm inequalities, several mean-square exponential stability criteria are established in terms of the formula and Razumikhin theorem to guarantee the stochastic interval delayed cellular neural networks to be mean-square exponential stable. Some recent results reported in the literatures are generalized. A kind of equivalent description for this stochastic interval cellular neural networks with time-varying delay is also given.

scholarly journals Almost Automorphic Functions of Ordernand Applications to Dynamic Equations on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Gisèle Mophou ◽  
Gaston Mandata N’Guérékata ◽  
Aril Milce
Keyword(s):  
Time Scales ◽  
Existence And Uniqueness ◽  
Dynamical Equation ◽  
Time Varying ◽  
First Order ◽  
Time Varying Delay ◽  
Almost Automorphic ◽  
Almost Automorphic Functions ◽  
Varying Delay ◽  
Automorphic Functions

We revisit the notion on almost automorphic functions on time scales given by Lizama and Mesquita (2013). Then we present the notion of almost automorphic functions of ordern. Finally, we apply this notion to study the existence and uniqueness and the global stability of almost automorphic solution of first order to a dynamical equation with finite time varying delay.

Guaranteed Cost Synchronization of Chaotic Cellular Neural Networks with Time-Varying Delay

2012 ◽  
Vol 24 (1) ◽  
pp. 217-233 ◽  
Author(s):  
Jianjun Tu ◽  
Hanlin He
Keyword(s):  
Neural Networks ◽  
Cellular Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Razumikhin Theorem ◽  
Time Varying Delay ◽  
Analysis Process ◽  
Guaranteed Cost ◽  
Varying Delay

Synchronization of cellular neural networks with time-varying delay is discussed in this letter. Based on Razumikhin theorem, a guaranteed cost synchronous controller is given. Unlike Lyapunov-Krasovskii analysis process, there is no constraint on the change rate of time delay. The saturated terms emerging in the Razumikhin analysis are amplified by zoned discussion and maximax synthesis rather than by Lipschitz condition and vector inequality, which will bring more conservatism. Then the controller criterion is transformed from quadratic matrix inequality form into linear matrix inequality form, with the help of a sufficient and necessary transformation condition. The minimization of the guaranteed cost is studied, and a further criterion for getting the controller is presented. Finally, the guaranteed cost synchronous control and its corresponding minimization problem are illustrated with examples of chaotic time-varying delay cellular neural networks.

scholarly journals Improved Stability Criteria for Time-Varying Delay System Using Second and First Order Polynomials

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 210961-210969
Author(s):  
Sharat Chandra Mahto ◽  
Rajvikram Madurai Elavarasan ◽  
Sandip Ghosh ◽  
R. K. Saket ◽  
Eklas Hossain ◽  
...  
Keyword(s):  
Delay System ◽  
Time Varying ◽  
Stability Criteria ◽  
First Order ◽  
Time Varying Delay ◽  
Improved Stability ◽  
Varying Delay
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