scholarly journals Controllability of conformable differential systems

2020 ◽  
Vol 25 (4) ◽  
Author(s):  
Xiaowen Wang ◽  
JinRong Wang ◽  
Michal Fečkan
Keyword(s):  
Fixed Point ◽  
Necessary Conditions ◽  
Complete Controllability ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Differential Systems ◽  
Numerical Examples ◽  
Controllability Of Systems ◽  
Sufficient And Necessary Conditions ◽  
Theoretical Results ◽  
Controllability Result

This paper deals with complete controllability of systems governed by linear and semilinear conformable differential equations. By establishing conformable Gram criterion and rank criterion, we give sufficient and necessary conditions to examine that a linear conformable system is null completely controllable. Further, we apply Krasnoselskii’s fixed point theorem to derive a completely controllability result for a semilinear conformable system. Finally, three numerical examples are given to illustrate our theoretical results.  

scholarly journals Controllability of Differential Systems with the General Conformable Derivative

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Ferrag Azouz ◽  
Djalal Boucenna ◽  
Abdellatif Ben Makhlouf ◽  
Lassaad Mchiri ◽  
Abbes Benchaabane
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Necessary Conditions ◽  
Order System ◽  
Complete Controllability ◽  
Conformable Derivative ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Differential Systems ◽  
Sufficient And Necessary Conditions ◽  
Controllability Result

In this paper, the controllability of differential systems with the general conformable derivative is studied. By elaborating the rank criterion and the conformable Gram criterion, sufficient and necessary conditions to investigate that a linear general conformable system is null completely controllable are given. We obtain a full generalization to the general conformable fractional-order system case. In addition, Krasnoselskii’s fixed point theorem to obtain a complete controllability result for a semilinear general conformable system is applied.

scholarly journals Controllability of Multiagent Systems with a Directed Tree

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Li Wang ◽  
Xiao Han
Keyword(s):  
Multiagent Systems ◽  
Multiagent System ◽  
Necessary Conditions ◽  
New Method ◽  
Information Communication ◽  
Controllability Problem ◽  
Directed Tree ◽  
Numerical Examples ◽  
Sufficient And Necessary Conditions ◽  
Theoretical Results

This paper addresses the controllability problem of multiagent systems with a directed tree based on the classic agreement protocol, in which the information communication topologies being a directed tree and containing a directed tree are both investigated. Different from the literatures, a new method, the star transform, is proposed to study the controllability of multiagent systems with directed topology. Some sufficient and necessary conditions are given for the controllability of such multiagent system. Numerical examples and simulations are proposed to illustrate the theoretical results.

scholarly journals First-order impulsive differential systems: sufficient and necessary conditions for oscillatory or asymptotic behavior

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Shyam Sundar Santra ◽  
Dumitru Baleanu ◽  
Khaled Mohamed Khedher ◽  
Osama Moaaz
Keyword(s):  
Fixed Point ◽  
Asymptotic Behavior ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Differential Systems ◽  
First Order ◽  
Impulsive Differential Systems ◽  
Sufficient And Necessary Conditions

AbstractIn this paper, we study the oscillatory and asymptotic behavior of a class of first-order neutral delay impulsive differential systems and establish some new sufficient conditions for oscillation and sufficient and necessary conditions for the asymptotic behavior of the same impulsive differential system. To prove the necessary part of the theorem for asymptotic behavior, we use the Banach fixed point theorem and the Knaster–Tarski fixed point theorem. In the conclusion section, we mention the future scope of this study. Finally, two examples are provided to show the defectiveness and feasibility of the main results.

scholarly journals Controllability of Second-Order Multiagent Systems with Multiple Leaders and General Dynamics

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Bo Liu ◽  
Hongke Feng ◽  
Li Wang ◽  
Rong Li ◽  
Junyan Yu ◽  
...  
Keyword(s):  
Multiagent Systems ◽  
Multiagent System ◽  
Necessary Conditions ◽  
Second Order ◽  
The Other ◽  
Numerical Examples ◽  
General Dynamics ◽  
Sufficient And Necessary Conditions ◽  
Multiple Leaders ◽  
Theoretical Results

This paper proposes a new second-order discrete-time multiagent model and addresses the controllability of second-order multiagent system with multiple leaders and general dynamics. The leaders play an important role in governing the other member agents to achieve any desired configuration. Some sufficient and necessary conditions are given for the controllability of the second-order multiagent system. Moreover, the speed controllability of the second-order multiagent system with general dynamics is discussed. Particularly, it is shown that the controllability of the whole system relies on the number of leaders and the connectivity between the leaders and the members. Numerical examples illustrate the theoretical results.

scholarly journals Existence of Center for Planar Differential Systems with Impulsive Perturbations

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Dengguo Xu
Keyword(s):  
Computing Methods ◽  
Impulsive Systems ◽  
Differential Systems ◽  
Numerical Examples ◽  
State Dependent ◽  
Planar Systems ◽  
Linear And Nonlinear ◽  
Impulsive Perturbations ◽  
The Stability ◽  
Theoretical Results

We present a method that uses successor functions in ordinary differential systems to address the “center-focus” problem of a class of planar systems that have an impulsive perturbation. By deriving solution formulae for impulsive systems, several interesting criteria for distinguishing between the center and the focus of linear and nonlinear planar systems with state-dependent impulsions are established. The conditions describing the stability of the focus of the considered models are also given. The computing methods presented here are more convenient for determining the center of impulsive systems than those in the literature. Numerical examples are given to show the effectiveness of the theoretical results.

scholarly journals Controllability of Fractional Neutral Stochastic Integro-Differential Systems with Infinite Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Xichao Sun ◽  
Litan Yan ◽  
Jing Cui
Keyword(s):  
Fixed Point ◽  
Fractional Calculus ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Abstract Space ◽  
Differential Systems ◽  
Compactness Condition ◽  
Fixed Point Principle ◽  
Controllability Result

This paper is concerned with the controllability of a class of fractional neutral stochastic integro-differential systems with infinite delay in an abstract space. By employing fractional calculus and Sadovskii's fixed point principle without assuming severe compactness condition on the semigroup, a set of sufficient conditions are derived for achieving the controllability result.

A JOINT EOQ MODEL FOR SUPPLIER AND RETAILER WITH DETERIORATING ITEMS

2004 ◽  
Vol 21 (02) ◽  
pp. 163-178 ◽  
Author(s):  
CHINHO LIN ◽  
YIHSU LIN
Keyword(s):  
Necessary Conditions ◽  
Optimal Solution ◽  
Planning Horizon ◽  
Solution Procedure ◽  
Sensitivity Analyses ◽  
Mutual Cooperation ◽  
Total Cost ◽  
Numerical Examples ◽  
Eoq Model ◽  
Sufficient And Necessary Conditions

The paper studies the joint inventory model between supplier and retailer relying on mutual cooperation. Unlike other studies, the deteriorated rate and partial back-ordering are consistent with assumptions for dealing with more general cases. Since it is difficult to solve this problem directly, we derived the sufficient and necessary conditions in the planning horizon, and proposed a procedure to find the optimal solution. Numerical examples and sensitivity analyses are also provided to illustrate the solution procedure. The results reveal that the extensions of the model provide a wider and reasonable situation in practice, and that they also reduce the total cost.

scholarly journals Linear θ-Method and Compact θ-Method for Generalised Reaction-Diffusion Equation with Delay

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Fengyan Wu ◽  
Qiong Wang ◽  
Xiujun Cheng ◽  
Xiaoli Chen
Keyword(s):  
Diffusion Equation ◽  
Necessary Conditions ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Stability And Convergence ◽  
Asymptotically Stable ◽  
Sufficient And Necessary Conditions ◽  
Equation Solvability ◽  
Equation With Delay ◽  
Theoretical Results

This paper is concerned with the analysis of the linear θ-method and compact θ-method for solving delay reaction-diffusion equation. Solvability, consistence, stability, and convergence of the two methods are studied. When θ∈[0,1/2), sufficient and necessary conditions are given to show that the two methods are asymptotically stable. When θ∈[1/2,1], the two methods are proven to be unconditionally asymptotically stable. Finally, several examples are carried out to confirm the theoretical results.

scholarly journals MITTAG-LEFFLER STABILITY ANALYSIS OF TEMPERED FRACTIONAL NEURAL NETWORKS WITH SHORT MEMORY AND VARIABLE-ORDER

Fractals ◽  
2021 ◽  
pp. 2140029
Author(s):  
CHUAN-YUN GU ◽  
FENG-XIA ZHENG ◽  
BABAK SHIRI
Keyword(s):  
Neural Networks ◽  
Fixed Point ◽  
Stability Analysis ◽  
Fixed Point Theorem ◽  
Banach Fixed Point Theorem ◽  
Stability Conditions ◽  
Variable Order ◽  
Numerical Examples ◽  
Short Memory ◽  
Theoretical Results

A class of tempered fractional neural networks is proposed in this paper. Stability conditions for tempered fractional neural networks are provided by using Banach fixed point theorem. Attractivity and Mittag-Leffler stability are given. In order to show the efficiency and convenience of the method used, tempered fractional neural networks with and without delay are discussed, respectively. Furthermore, short memory and variable-order tempered fractional neural networks are proposed under the global conditions. Finally, two numerical examples are used to demonstrate the theoretical results.

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