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.

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.

SIGNS OF REGULARITY AND STABILITY OF DIFFERENTIAL EQUATIONS OF HIGHER ORDER

2018 ◽  
pp. 674-678
Author(s):  
Anatoly Ivanovich Perov ◽  
Irina Dmitrievna Kostrub
Keyword(s):  
Differential Equations ◽  
Main Part ◽  
Higher Order ◽  
Matrix Differential Equations ◽  
Matrix Differential ◽  
Vector Matrix

On the basis of previous works of authors new signs of regularity and stability of vector-matrix differential equations with a variable main part are specified.

An oscillation theorem for self-adjoint differential systems and an index result for corresponding Riccati matrix differential equations

1995 ◽  
Vol 118 (2) ◽  
pp. 351-361 ◽  
Author(s):  
Werner Kratz
Keyword(s):  
Index Formula ◽  
Oscillation Theorem ◽  
Differential Systems ◽  
Eigenvalue Parameter ◽  
Matrix Differential Equations ◽  
The Difference ◽  
Matrix Differential ◽  
The Given ◽  
Conjoined Basis ◽  
Riccati Matrix

AbstractThe main result of this paper is an oscillation theorem on linear self-adjoint differential systems and a corresponding eigenvalue problem. It establishes a formula between the number of focal points of a so-called conjoined basis of the differential system on a given compact interval and the number of eigenvalues which are less than the given eigenvalue parameter. It extends an earlier result of the author and generalizes an oscillation theorem of M. Morse. Among others the proof of the theorem requires a formula on the index of the difference of symmetric solutions of a corresponding Riccati matrix differential equation. This index formula is the other new result presented.

On differential equations in Banach algebras

2020 ◽  
pp. 410-421
Author(s):  
Anatoly I. Perov ◽  
Irina D. Kostrub
Keyword(s):  
Differential Equations ◽  
Banach Algebras ◽  
Higher Order ◽  
Original Research ◽  
Matrix Equations ◽  
Small Oscillations ◽  
Matrix Differential Equations ◽  
Constant Coefficients ◽  
Linear Differential ◽  
Matrix Differential

We consider higher-order linear differential equations with constant coefficients in Banach algebras (this is a direct generalization of higher-order matrix differential equations). The presentation is based on higher algebra, differential equations and functional analysis. The results obtained can be used in the study of matrix equations, in the theory of small oscillations in physics, and in the theory of perturbations in quantum mechanics. The presentation is based on the original research of the authors.

scholarly journals Stability analysis of nonlinear Lyapunov systems associated with an nth order system of matrix differential equations

2002 ◽  
Vol 15 (2) ◽  
pp. 141-150
Author(s):  
K. N. Murty ◽  
Michael D. Shaw
Keyword(s):  
Stability Analysis ◽  
Sufficient Conditions ◽  
Order System ◽  
Lipschitz Stability ◽  
Differential Systems ◽  
Variation Of Parameters ◽  
Order Matrix ◽  
Matrix Differential Equations ◽  
Variation Of Parameters Formula ◽  
Matrix Differential

This paper introduces the notion of Lipschitz stability for nonlinear nth order matrix Lyapunov differential systems and gives sufficient conditions for Lipschitz stability. We develop variation of parameters formula for the solution of the nonhomogeneous nonlinear nth order matrix Lyapunov differential system. We study observability and controllability of a special system of nth order nonlinear Lyapunov systems.

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