scholarly journals Analysis of a Class of Fractional Nonlinear Multidelay Differential Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-15
Author(s):  
Zhuoyan Gao ◽  
JinRong Wang ◽  
Yong Zhou
Keyword(s):  
Iterative Learning Control ◽  
Time Delays ◽  
Iterative Learning ◽  
Multiple Time ◽  
Weighted Norm ◽  
Differential Systems ◽  
Numerical Examples ◽  
Multiple Time Delays ◽  
Two Parameters ◽  
Theoretical Results

We address existence and Ulam-Hyers and Ulam-Hyers-Mittag-Leffler stability of fractional nonlinear multiple time-delays systems with respect to two parameters’ weighted norm, which provides a foundation to study iterative learning control problem for this system. Secondly, we design PID-type learning laws to generate sequences of output trajectories to tracking the desired trajectory. Two numerical examples are used to illustrate the theoretical results.

PD-Type ILC Algorithm Research with Forgetting Factor for a Class of Linear Systems with Multiple Time Delays

2012 ◽  
Vol 220-223 ◽  
pp. 1125-1130 ◽  
Author(s):  
Hong Yang ◽  
Sheng Ming Li
Keyword(s):  
Linear Systems ◽  
Iterative Learning Control ◽  
Time Delays ◽  
Learning Control ◽  
Iterative Learning ◽  
Multiple Time ◽  
Forgetting Factor ◽  
Convergence Conditions ◽  
Multiple Time Delays ◽  
Study Results

Based on iterative learning control (ILC) algorithm with forgetting factor, the thought that the forgetting factor is a function of iteration numbers is proposed in this paper, which has simplified the convergence conditions. And the convergence analysis is given. Then, the study results of this paper are applied to a class of linear systems with multiple time delays and simulation results show that, under the improvements of the convergence conditions and the reasonable choice of forgetting factor function, the PD-type iterative learning control algorithm with forgetting factor applied to the linear systems with multiple time delays in this paper has effectiveness and superiority.

Bifurcation, Synchronization, and Multistability of Two Interacting Networks with Multiple Time Delays

2016 ◽  
Vol 26 (09) ◽  
pp. 1650156 ◽  
Author(s):  
Xiaochen Mao
Keyword(s):  
Time Delays ◽  
Nearest Neighbor ◽  
Pitchfork Bifurcation ◽  
Multiple Time ◽  
Multiple Time Delays ◽  
Trivial Equilibrium ◽  
Dynamical Properties ◽  
Interacting Networks ◽  
Delay Dependent ◽  
Theoretical Results

This paper reveals the dynamical properties of two interacting neural networks with multiple couplings. Different time delays are introduced into the nearest-neighbor links and long-range connections in each layer and the couplings between different substructures. The delay-dependent and delay-independent stability and the oscillations bifurcated from the trivial equilibrium of the network are analyzed. The conditions of the existence of nontrivial equilibria and pitchfork bifurcation are discussed. Numerical simulations are performed to validate the theoretical results and interesting neuronal activities are observed, such as completely synchronous oscillations, three types of asynchronous oscillations, multiple switches between the rest states and different oscillations, coexistence of different oscillations, and coexistence of nontrivial equilibria and oscillations.

scholarly journals Stability analysis of linear neutral systems with multiple time delays

2005 ◽  
Vol 2005 (2) ◽  
pp. 175-183 ◽  
Author(s):  
Keyue Zhang
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Spectral Radius ◽  
Time Delays ◽  
Multiple Time ◽  
Stability Criteria ◽  
Neutral Systems ◽  
Numerical Examples ◽  
Multiple Time Delays ◽  
New Criteria

This paper studies the asymptotic stability of linear neutral systems with multiple time delays. Using the characteristic equation of the system, new delay-independent stability criteria are derived in terms of the spectral radius of modulus matrices. Numerical examples are given to demonstrate the validity of our new criteria.

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