scholarly journals Solutions of Higher-Order Homogeneous Linear Matrix Differential Equations for Consistent and Non-Consistent Initial Conditions: Regular Case

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Ioannis K. Dassios
Keyword(s):  
Differential Equations ◽  
Initial Conditions ◽  
Matrix Pencil ◽  
Higher Order ◽  
Linear Matrix ◽  
Regular Case ◽  
Numerical Examples ◽  
Matrix Differential Equations ◽  
Matrix Differential ◽  
Homogeneous Linear

We study a class of linear matrix differential equations (regular case) of higher order whose coefficients are square constant matrices. By using matrix pencil theory and the Weierstrass canonical form of the pencil we obtain formulas for the solutions and we show that the solution is unique for consistent initial conditions and infinite for nonconsistent initial conditions. Moreover we provide some numerical examples. These kinds of systems are inherent in many physical and engineering phenomena.

scholarly journals Solution Properties of Linear Descriptor (Singular) Matrix Differential Systems of Higher Order with (Non-) Consistent Initial Conditions

2010 ◽  
Vol 2010 ◽  
pp. 1-24 ◽  
Author(s):  
Athanasios A. Pantelous ◽  
Athanasios D. Karageorgos ◽  
Grigoris I. Kalogeropoulos ◽  
Kostas G. Arvanitis
Keyword(s):  
System Theory ◽  
General Class ◽  
Initial Conditions ◽  
Higher Order ◽  
Solution Properties ◽  
Singular Matrix ◽  
Differential Systems ◽  
Matrix Differential Equations ◽  
Matrix Differential ◽  
Time Invariant

In some interesting applications in control and system theory, linear descriptor (singular) matrix differential equations of higher order with time-invariant coefficients and (non-) consistent initial conditions have been used. In this paper, we provide a study for the solution properties of a more general class of the Apostol-Kolodner-type equations with consistent and nonconsistent initial conditions.

Sign in / Sign up

Export Citation Format

Share Document