scholarly journals Controllability and Observability of Fractional Linear Systems with Two Different Orders

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Dengguo Xu ◽  
Yanmei Li ◽  
Weifeng Zhou
Keyword(s):  
Dynamical Systems ◽  
Linear Systems ◽  
Necessary Conditions ◽  
Sufficient And Necessary Conditions ◽  
State Observability ◽  
Controllability And Observability

This paper is concerned with the controllability and observability for a class of fractional linear systems with two different orders. The sufficient and necessary conditions for state controllability and state observability of such systems are established. The results obtained extend some existing results of controllability and observability for fractional dynamical systems.

scholarly journals Reachability and Controllability of Fractional Singular Dynamical Systems with Control Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Hai Zhang ◽  
Jinde Cao ◽  
Wei Jiang
Keyword(s):  
Dynamical Systems ◽  
Necessary Conditions ◽  
Algebraic Approach ◽  
Coefficient Matrix ◽  
The State ◽  
State Structure ◽  
Singular Coefficient ◽  
Control Delay ◽  
State Response ◽  
Sufficient And Necessary Conditions

This paper is concerned with the reachability and controllability of fractional singular dynamical systems with control delay. The factors of such systems including the Caputo’s fractional derivative, control delay, and singular coefficient matrix are taken into account synchronously. The state structure of fractional singular dynamical systems with control delay is characterized by analysing the state response and reachable set. A set of sufficient and necessary conditions of controllability for such systems are established based on the algebraic approach. Moreover, an example is provided to illustrate the effectiveness and applicability of the proposed criteria.

Full-Column Rank Solutions to a Nonlinear Matrix Equation

2012 ◽  
Vol 490-495 ◽  
pp. 1265-1268 ◽  
Author(s):  
Yan Tao Wang ◽  
Xin Rong Yang ◽  
Rui Zhi Zhang
Keyword(s):  
Linear Systems ◽  
Matrix Equation ◽  
Continuous Time ◽  
Necessary Conditions ◽  
Full Rank ◽  
Full Column Rank ◽  
Nonlinear Matrix Equation ◽  
Sufficient And Necessary Conditions ◽  
Nonlinear Matrix ◽  
Descriptor Linear Systems

This paper concerns full-column rank solutions to the nonlinear matrix equation XA+XBX=HX, which is proposed from the so-called regulation problem of continuous-time (descriptor) linear systems with constrained states and controls. Sufficient and necessary conditions under which the nonlinear matrix equation has at least one full rank solution are investigated, and thereby, a mistake in [1] is pointed out by constructing a counterexample. Moreover, one full-column rank solutions to the nonlinear matrix equation is constructed.

scholarly journals Controllability Criteria for Linear Fractional Differential Systems with State Delay and Impulses

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Hai Zhang ◽  
Jinde Cao ◽  
Wei Jiang
Keyword(s):  
Fractional Derivative ◽  
Linear Systems ◽  
Necessary Conditions ◽  
State Delay ◽  
Differential Systems ◽  
State Response ◽  
Fractional Differential Systems ◽  
Sufficient And Necessary Conditions ◽  
Fractional Differential ◽  
Controllability Property

This paper is concerned with the controllability of linear fractional differential systems with delay in state and impulses. The factors of such systems including fractional derivative, impulses, and delay are taken into account synchronously. The expression of state response for such systems is derived, and the sufficient and necessary conditions of controllability criteria are established. Both the proposed criteria and illustrative examples show that the controllability property of the linear systems is dependent neither on the order of fractional derivative, on delay nor on impulses.

scholarly journals Oscillation of Second-Order Differential Equations with Multiple and Mixed Delays under a Canonical Operator

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1323
Author(s):  
Shyam Sundar Santra ◽  
Rami Ahmad El-Nabulsi ◽  
Khaled Mohamed Khedher
Keyword(s):  
Differential Equations ◽  
Necessary Conditions ◽  
Second Order ◽  
Multiple Delays ◽  
Mixed Delays ◽  
Neutral Differential Equations ◽  
Canonical Operator ◽  
Second Order Differential Equations ◽  
The Future ◽  
Sufficient And Necessary Conditions

In this work, we obtained new sufficient and necessary conditions for the oscillation of second-order differential equations with mixed and multiple delays under a canonical operator. Our methods could be applicable to find the sufficient and necessary conditions for any neutral differential equations. Furthermore, we proved the validity of the obtained results via particular examples. At the end of the paper, we provide the future scope of this study.

scholarly journals Properties of Certain Subclass of Meromorphic Multivalent Functions Associated with q-Difference Operator

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1035
Author(s):  
Cai-Mei Yan ◽  
Rekha Srivastava ◽  
Jin-Lin Liu
Keyword(s):  
Difference Operator ◽  
Necessary Conditions ◽  
Partial Sums ◽  
Coefficient Estimates ◽  
Radius Of Starlikeness ◽  
Closure Theorems ◽  
Sufficient And Necessary Conditions ◽  
Distortion Theorems ◽  
Growth And Distortion Theorems

A new subclass Σp,q(α,A,B) of meromorphic multivalent functions is defined by means of a q-difference operator. Some properties of the functions in this new subclass, such as sufficient and necessary conditions, coefficient estimates, growth and distortion theorems, radius of starlikeness and convexity, partial sums and closure theorems, are investigated.

Perfect colorings of patterns with multiple orbits

2019 ◽  
Vol 75 (6) ◽  
pp. 814-826
Author(s):  
Allan Junio ◽  
Ma. Lailani Walo
Keyword(s):  
Necessary Conditions ◽  
Sufficient And Necessary Conditions

This paper studies colorings of patterns with multiple orbits, particularly those colorings where the orbits share colors. The main problem is determining when such colorings become perfect. This problem is attacked by characterizing all perfect colorings of patterns through the construction of sufficient and necessary conditions for a coloring to be perfect. These results are then applied on symmetrical objects to construct both perfect and non-perfect colorings.

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