The Benefits of Schooling: A Human Capital Alocation into a Continuous Optimal Control Framework

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Discretizing LTI Descriptor (Regular) Differential Input Systems with Consistent Initial Conditions

A technique for discretizing efficiently the solution of a Linear descriptor (regular) differential input system with consistent initial conditions, and Time-Invariant coefficients (LTI) is introduced and fully discussed. Additionally, an upper bound for the error ‖x¯(kT)−x¯k‖ that derives from the procedure of discretization is also provided. Practically speaking, we are interested in such kind of systems, since they are inherent in many physical, economical and engineering phenomena

AN ANGLE METRIC THROUGH THE NOTION OF GRASSMANN REPRESENTATIVE

The present paper has two main goals. Firstly, to introduce different metric topologies on the pencils (F, G) associated with autonomous singular (or regular) linear differential or difference systems. Secondly, to establish a new angle metric which is described by decomposable multi-vectors called Grassmann representatives (or Plücker coordinates) of the corresponding subspaces. A unified framework is provided by connecting the new results to known ones, thus aiding in the deeper understanding of various structural aspects of matrix pencils in system theory

Transferring instantly the state of a linear singular descriptor differential system

In numerous computational applications in mechanics, in engineering, as well as, in financial issues, the ability of manipulating instantly the state vector from the input is more than significant. Thus, in this paper, we extend a method for the instantly state transferring of linear singular descriptor differential systems, which is based on impulsive distributions. Using linear algebra techniques and the generalized inverse theory, the input’s coefficients are determined

Symmetric/skew-symmetric homogeneous matrix descriptor (regular) differential systems with consistent initial conditions

This paper introduces the results of Thompson’s canonical form under congruence for pairs of complex matrices with symmetric and skew symmetric structural properties to the solution of higher order linear matrix homogeneous differential systems. Under this approach, the main equation is divided into five sub-systems whose solutions are derived. Note that the regularity or singularity of matrix pencil predetermines the number of sub-systems. The special properties of such systems may be appeared in engineering and even in some financial models

Power series solutions for linear higher order rectangular differential matrix control systems

This paper is concerned with the solution of linear higher order rectangular differential matrix systems which are appeared in many applications of optimal and filtering control theory. The classical power series method is employed to obtain the analytic solution of linear higher order rectangular (singular) differential matrix equations. In the present paper, the authors provide some preliminary results for solving linear singular matrix systems with the power series approach

Error Analysis of the Complex Kronecker Canonical Form

In some interesting applications in control and system theory, i.e. in engineering, in ecology (Leslie population model), in financial/actuarial (Leontief multi input - multi output) science, linear descriptor (singular) differential/difference equations with time-invariant coefficients and (non-) consistent initial conditions have been extensively used. The solution properties of those systems are based on the Kronecker canonical form, which is an important component of the Matrix Pencil Theory. In this paper, we present some preliminary results for the error analysis of the complex Kronecker canonical form based on the Euclidean norm. Finally, under some weak assumptions an interesting new necessary condition is also derived

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

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