Partial reduction for linear systems of operator equations with system matrix in companion form

2015 ◽  
Vol 45 (2) ◽  
pp. 1-9
Author(s):  
Ivana Jovović
Keyword(s):  
Linear Systems ◽  
Partial Reduction ◽  
System Matrix ◽  
Operator Equations

scholarly journals Formulae of partial reduction for linear systems of first order operator equations

2010 ◽  
Vol 23 (11) ◽  
pp. 1367-1371 ◽  
Author(s):  
Branko Malešević ◽  
Dragana Todorić ◽  
Ivana Jovović ◽  
Sonja Telebaković
Keyword(s):  
Linear Systems ◽  
Partial Reduction ◽  
Order Operator ◽  
Operator Equations ◽  
First Order

scholarly journals Total reduction of linear systems of operator equations with the system matrix in the companion form

2013 ◽  
Vol 93 (107) ◽  
pp. 117-126
Author(s):  
Ivana Jovovic
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Characteristic Matrix ◽  
System Matrix ◽  
Operator Equations ◽  
Total Reduction ◽  
System Of Operator Equations ◽  
Separated Variables

We consider a total reduction of a nonhomogeneous linear system of operator equations with the system matrix in the companion form. Totally reduced system obtained in this manner is completely decoupled, i.e., it is a system with separated variables. We introduce a method for the total reduction, not by a change of basis, but by finding the adjugate matrix of the characteristic matrix of the system matrix. We also indicate how this technique may be used to connect differential transcendence of the solution with the coefficients of the system.

scholarly journals Preconditioning for Sparse Linear Systems at the Dawn of the 21st Century: History, Current Developments, and Future Perspectives

2012 ◽  
Vol 2012 ◽  
pp. 1-49 ◽  
Author(s):  
Massimiliano Ferronato
Keyword(s):  
Linear Systems ◽  
Specific Problem ◽  
General Purpose ◽  
Sparse Linear Systems ◽  
System Matrix ◽  
Preconditioning Techniques ◽  
Key Factor ◽  
Recent Developments ◽  
Approximate Inverses ◽  
Linear Systems Of Equations

Iterative methods are currently the solvers of choice for large sparse linear systems of equations. However, it is well known that the key factor for accelerating, or even allowing for, convergence is the preconditioner. The research on preconditioning techniques has characterized the last two decades. Nowadays, there are a number of different options to be considered when choosing the most appropriate preconditioner for the specific problem at hand. The present work provides an overview of the most popular algorithms available today, emphasizing the respective merits and limitations. The overview is restricted to algebraic preconditioners, that is, general-purpose algorithms requiring the knowledge of the system matrix only, independently of the specific problem it arises from. Along with the traditional distinction between incomplete factorizations and approximate inverses, the most recent developments are considered, including the scalable multigrid and parallel approaches which represent the current frontier of research. A separate section devoted to saddle-point problems, which arise in many different applications, closes the paper.

scholarly journals Input retrieval in finite dimensional linear systems

1982 ◽  
Vol 23 (4) ◽  
pp. 357-382 ◽  
Author(s):  
P. G. Howlett
Keyword(s):  
Linear Systems ◽  
Type System ◽  
System Matrix ◽  
Fundamental Idea ◽  
Finite Dimensional ◽  
First Case ◽  
Direct Linkage ◽  
Explicit Formulae ◽  
Output Only ◽  
General Method

AbstractFor finite dimensional linear systems it is known that in certain circumstances the input can be retrieved from a knowledge of the output only. The main aim of this paper is to produce explicit formulae for input retrieval in systems which do not possess direct linkage from input to output. Although two different procedures are suggested the fundamental idea in both cases is to find an expression for the inverse transfer function of the system. In the first case this is achieved using a general method of power series inversion and in the second case by a sequence of elementary operations on a Rosenbrock type system matrix.

scholarly journals Differential transcendence of solutions of systems of linear differential equations based on total reduction of the system

2020 ◽  
pp. 24-24
Author(s):  
Ivana Jovovic
Keyword(s):  
Linear System ◽  
Differential Equations ◽  
Complex Field ◽  
System Matrix ◽  
Operator Equations ◽  
Total Reduction ◽  
Commuting Operators ◽  
Constant Coefficients ◽  
Linear Differential ◽  
System Of Operator Equations

In this paper we consider total reduction of the nonhomogeneous linear system of operator equations with constant coefficients and commuting operators. The totally reduced system obtained in this manner is completely decoupled. All equations of the system differ only in the variables and in the nonhomogeneous terms. The homogeneous parts are obtained using the generalized characteristic polynomial of the system matrix. We also indicate how this technique may be used to examine differential transcendence of the solution of the linear system of the differential equations with constant coefficients over the complex field and meromorphic free terms.

scholarly journals HIGHER-ORDER SLIDING MODE DYNAMICS DESIGN FOR A CLASS OF SINGLE-INPUT LINEAR SYSTEMS

2020 ◽  
Vol 19 (2) ◽  
pp. 103
Author(s):  
Boban Veselić
Keyword(s):  
Linear Systems ◽  
Sliding Mode ◽  
Higher Order ◽  
System Matrix ◽  
Sliding Manifold ◽  
Single Input ◽  
Digital Simulations ◽  
Specific Sliding ◽  
Sliding Mode Dynamics ◽  
Mode Order

The paper considers a higher-order sliding mode dynamics design in a class of single-input linear systems having the invertible system matrix. The proposed sliding manifold selection method simultaneously provides a necessary relative degree of the sliding variable for a specific sliding mode order and the desired system dynamics after establishing that sliding mode. It is shown that the found unique solution satisfies these requirements. The theoretically obtained result is validated through a numerical example and illustrated by digital simulations.

Optimal Redesign of Linear Systems

1996 ◽  
Vol 118 (3) ◽  
pp. 598-605 ◽  
Author(s):  
K. M. Grigoriadis ◽  
G. Zhu ◽  
R. E. Skelton
Keyword(s):  
Quadratic Programming ◽  
Linear Systems ◽  
Covariance Matrix ◽  
Active Control ◽  
Closed Loop ◽  
Controller Design ◽  
Iterative Approach ◽  
System Matrix ◽  
Closed Loop System ◽  
Control Effort

This paper proposes a redesign procedure for linear systems. We suppose that an initial satisfactory controller which yields the desired performance is given. Then both the plant and the controller are redesigned to minimize the required active control effort. Either the closed-loop system matrix or the closed-loop covariance matrix of the initial design can be preserved under the redesign. Convex quadratic programming solves this problem. In addition, an iterative approach for integrated plant and controller design is proposed, which uses the above optimal plant/controller redesign in each iterative step. The algorithm has guaranteed convergence and provides a sequence of designs with monotonically decreasing active control effort. Examples are included to illustrate the procedure.

scholarly journals A note on the reduction formulas for some systems of linear operator equations

Filomat ◽  
2016 ◽  
Vol 30 (5) ◽  
pp. 1353-1362
Author(s):  
Ivana Jovovic ◽  
Branko Malesevic
Keyword(s):  
Linear System ◽  
Linear Operator ◽  
The Other ◽  
Characteristic Matrix ◽  
System Matrix ◽  
Operator Equations ◽  
Rational Form ◽  
Total Reduction ◽  
Linear Operator Equations

We consider partial and total reduction of a nonhomogeneous linear system of the operator equations with the system matrix in the same particular form as in paper [7]. Here we present two different concepts. One is concerned with partially reduced systems obtained by using the Jordan and the rational form of the system matrix. The other one is dealing with totally reduced systems obtained by finding the adjugate matrix of the characteristic matrix of the system matrix.

scholarly journals LINEAR SYSTEMS OF DIFFERENTIAL EQUATIONS IN ARROWHEAD FORM

2021 ◽  
pp. 557
Author(s):  
Ivana Jovović
Keyword(s):  
Differential Equations ◽  
Linear Systems ◽  
Characteristic Matrix ◽  
System Matrix ◽  
First Order ◽  
Systems Of Differential Equations ◽  
Algebraic Properties ◽  
Arrowhead Matrix ◽  
Invariant Factors ◽  
First Order Differential Equations

This paper deals with different approaches for solving linear systems of the first order differential equations with the system matrix in the symmetric arrowhead form.Some needed algebraic properties of the symmetric arrowhead matrix are proposed.We investigate the form of invariant factors of the arrowhead matrix.Also the entries of the adjugate matrix of the characteristic matrix of the arrowhead matrix are considered. Some reductions techniques for linear systems of differential equations with the system matrix in the arrowhead form are presented.

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