scholarly journals Solving Fully Fuzzy Linear System with the Necessary and Sufficient Condition to have a Positive Solution

2014 ◽  
Vol 8 (3) ◽  
pp. 1003-1019 ◽  
Author(s):  
Ghassan Malkawi ◽  
Nazihah Ahmad ◽  
Haslinda Ibrahim
Keyword(s):  
Linear System ◽  
Positive Solution ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Fully Fuzzy Linear System ◽  
Fuzzy Linear System ◽  
Necessary And Sufficient

scholarly journals A Preconditioning Algorithm for the Positive Solution of Fully Fuzzy Linear System

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Kumar Dookhitram ◽  
Sameer Sunhaloo ◽  
Nisha Rambeerich ◽  
Arshad Peer ◽  
Aslam Saib
Keyword(s):  
Linear System ◽  
Positive Solution ◽  
Fully Fuzzy Linear System ◽  
Fuzzy Linear System

scholarly journals Plug and Play Robust Distributed Control with Ellipsoidal Parametric Uncertainty System

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Hong Wang-jian ◽  
Wang Yan-xiang
Keyword(s):  
Linear System ◽  
Distributed Control ◽  
Control Strategy ◽  
State Feedback ◽  
Parametric Uncertainty ◽  
State Feedback Control ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Plug And Play ◽  
Necessary And Sufficient

We consider a continuous linear time invariant system with ellipsoidal parametric uncertainty structured into subsystems. Since the design of a local controller uses only information on a subsystem and its neighbours, we combine the plug and play idea and robust distributed control to propose one distributed control strategy for linear system with ellipsoidal parametric uncertainty. Firstly for linear system with ellipsoidal parametric uncertainty, a necessary and sufficient condition for robust state feedback control is proposed by means of linear matrix inequality. If this necessary and sufficient condition is satisfied, this robust state feedback gain matrix can be easily derived to guarantee robust stability and prescribed closed loop performance. Secondly the plug and play idea is introduced in the design process. Finally by one example of aircraft flutter model parameter identification, the efficiency of the proposed control strategy can be easily realized.

On the Controllability of Distributed-Order Fractional Systems With Distributed Delays

2017 ◽  
Author(s):  
Bin-Bin He ◽  
YangQuan Chen ◽  
Chun-Hai Kou
Keyword(s):  
Nonlinear System ◽  
Linear System ◽  
Distributed Delays ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Fractional Systems ◽  
Gramian Matrix ◽  
Controllability Gramian ◽  
Necessary And Sufficient ◽  
Distributed Order

This paper investigates the controllability of distributed-order fractional systems with distributed delays. By using the controllability Gramian matrix and reduction to absurdity, a necessary and sufficient condition for the controllability of linear system is established, and a sufficient condition for the nonlinear system is obtained. Examples are given to illustrate the effectiveness of the theorems.

scholarly journals INHOMOGENEOUS PERIODIC PARABOLIC PROBLEMS WITH INDEFINITE DATA

2011 ◽  
Vol 84 (3) ◽  
pp. 516-524 ◽  
Author(s):  
T. GODOY ◽  
U. KAUFMANN
Keyword(s):  
Positive Solution ◽  
Bounded Domain ◽  
Parabolic Problems ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Smooth Bounded Domain ◽  
Unbounded Function ◽  
Existence Of Positive Solutions ◽  
Carathéodory Function ◽  
Necessary And Sufficient

AbstractLet Ω⊂ℝN be a smooth bounded domain and let f⁄≡0 be a possibly discontinuous and unbounded function. We give a necessary and sufficient condition on f for the existence of positive solutions for all λ>0 of Dirichlet periodic parabolic problems of the form Lu=h(x,t,u)+λf(x,t), where h is a nonnegative Carathéodory function that is sublinear at infinity. When this condition is not fulfilled, under some additional assumptions on h we characterize the set of λs for which the aforementioned problem possesses some positive solution. All results remain true for the corresponding elliptic problems.

scholarly journals Existence of blowup solutions for nonlinear problems with a gradient term

2006 ◽  
Vol 2006 ◽  
pp. 1-11 ◽  
Author(s):  
Faten Toumi
Keyword(s):  
Continuous Function ◽  
Positive Solution ◽  
Nonlinear Problems ◽  
Gradient Term ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Whole Space ◽  
Necessary And Sufficient

We prove the existence of positive explosive solutions for the equationΔu+λ(|x|)|∇u(x)|=ϕ(x,u(x))in the whole spaceℝN(N≥3), whereλ:[0,∞)→[0,∞)is a continuous function andϕ:ℝN×[0,∞)→[0,∞)is required to satisfy some hypotheses detailed below. More precisely, we will give a necessary and sufficient condition for the existence of a positive solution that blows up at infinity.

scholarly journals A Note on Solutions of Linear Systems

ISRN Algebra ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Branko Malešević ◽  
Ivana Jovović ◽  
Milica Makragić ◽  
Biljana Radičić
Keyword(s):  
Linear System ◽  
General Solution ◽  
Linear Systems ◽  
Sufficient Condition ◽  
Matrix Equations ◽  
Necessary And Sufficient Condition ◽  
Different Types ◽  
Free Parameters ◽  
Necessary And Sufficient

We will consider Rohde's general form of {1}-inverse of a matrix A. The necessary and sufficient condition for consistency of a linear system Ax=c will be represented. We will also be concerned with the minimal number of free parameters in Penrose's formula x=A(1)c+(I-A(1)A)y for obtaining the general solution of the linear system. These results will be applied for finding the general solution of various homogenous and nonhomogenous linear systems as well as for different types of matrix equations.

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