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 Positifitas dan Ketercapaian Sistem Linier Fractional Waktu Kontinu

CAUCHY ◽  
2011 ◽  
Vol 2 (1) ◽  
pp. 18
Author(s):  
Imam Fahcruddin
Keyword(s):  
Continuous Time ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Positive Systems ◽  
Necessary And Sufficient Condition ◽  
Fractional Systems ◽  
Necessary And Sufficient

<div class="standard"><a id="magicparlabel-2384">This paper studies a solution of the fractional continuous-time linier system. Necessary and sufficient condition were established for the internal and external positivity of fractional systems. Sufficient conditions are given for the reachability of fractional positive systems. </a></div>

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.

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.

A Proposed Framework Emphasizing Auditor Reliability over Auditor Independence

2003 ◽  
Vol 17 (3) ◽  
pp. 257-266 ◽  
Author(s):  
Mark H. Taylor ◽  
F. Todd DeZoort ◽  
Edward Munn ◽  
Martha Wetterhall Thomas
Keyword(s):  
Public Interest ◽  
Auditor Independence ◽  
Public Confidence ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Accounting Profession ◽  
The Public ◽  
Necessary And Sufficient

This paper introduces an auditor reliability framework that repositions the role of auditor independence in the accounting profession. The framework is motivated in part by widespread confusion about independence and the auditing profession's continuing problems with managing independence and inspiring public confidence. We use philosophical, theoretical, and professional arguments to argue that the public interest will be best served by reprioritizing professional and ethical objectives to establish reliability in fact and appearance as the cornerstone of the profession, rather than relationship-based independence in fact and appearance. This revised framework requires three foundation elements to control subjectivity in auditors' judgments and decisions: independence, integrity, and expertise. Each element is a necessary but not sufficient condition for maximizing objectivity. Objectivity, in turn, is a necessary and sufficient condition for achieving and maintaining reliability in fact and appearance.

The Power of Public Positions

2018 ◽  
Author(s):  
Thomas Sinclair
Keyword(s):  
Detailed Analysis ◽  
Political Authority ◽  
The State ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
State Institutions ◽  
State Of Nature ◽  
Necessary And Sufficient

The Kantian account of political authority holds that the state is a necessary and sufficient condition of our freedom. We cannot be free outside the state, Kantians argue, because any attempt to have the “acquired rights” necessary for our freedom implicates us in objectionable relations of dependence on private judgment. Only in the state can this problem be overcome. But it is not clear how mere institutions could make the necessary difference, and contemporary Kantians have not offered compelling explanations. A detailed analysis is presented of the problems Kantians identify with the state of nature and the objections they face in claiming that the state overcomes them. A response is sketched on behalf of Kantians. The key idea is that under state institutions, a person can make claims of acquired right without presupposing that she is by nature exceptional in her capacity to bind others.

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