36 research outputs found
Discretizing LTI descriptor (regular) differential input systems with consistent initial conditions
No full textA 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)-xk∥ 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. Copyright © 2010 Athanasios D. Karageorgos et al
Transferring instantly the state of higher-order linear descriptor (Regular) differential systems using impulsive inputs
No full textIn many applications, and generally speaking in many dynamical differential systems, the problem of transferring the initial state of the system to a desired state in (almost) zero-time time is desirable but difficult to achieve. Theoretically, this can be achieved by using a linear combination of Dirac δ -function and its derivatives. Obviously, such an input is physically unrealizable. However, we can think of it approximately as a combination of small pulses of very high magnitude and infinitely small duration. In this paper, the approximation process of the distributional behaviour of higher-order linear descriptor (regular) differential systems is presented. Thus, new analytical formulae based on linear algebra methods and generalized inverses theory are provided. Our approach is quite general and some significant conditions are derived. Finally, a numerical example is presented and discussed. © 2009 Athanasios D. Karageorgos et al
The Drazin inverse through the matrix pencil approach and its application to the study of generalized linear systems with rectangular or square coefficient matrices
No full textIn several applications, e.g., in control and systems modeling theory, Drazin inverses and matrix pencil methods for the studyof generalized (descriptor) linear systems are used extensively. In this paper, a relation between the Drazin inverse and the Kronecker canonical form of rectangular pencils is derived and fullyin vestigated. Moreover, the relation between the Drazin inverse and the Weierstrass canonical form is revisited byp roviding a more algorithmic approach. Finally, the Weierstrass canonical form for a pencil through the core-nilpotent decomposition method is defined
Transferring Instantly the State of Higher-Order Linear Descriptor (Regular) Differential Systems Using Impulsive Inputs
No full textIn many applications, and generally speaking in many dynamical differential systems, the problem of transferring the initial state of the system to a desired state in (almost) zero-time time is desirable but difficult to achieve. Theoretically, this can be achieved by using a linear combination of Dirac -function and its derivatives. Obviously, such an input is physically unrealizable. However, we can think of it approximately as a combination of small pulses of very high magnitude and infinitely small duration. In this paper, the approximation process of the distributional behaviour of higher-order linear descriptor (regular) differential systems is presented. Thus, new analytical formulae based on linear algebra methods and generalized inverses theory are provided. Our approach is quite general and some significant conditions are derived. Finally, a numerical example is presented and discussed
Higher-order linear matrix descriptor differential equations of Apostol-Kolodner type
No full textIn this article, we study a class of linear rectangular matrix descriptor differential equations of higher-order whose coefficients are square constant matrices. Using the Weierstrass canonical form, the analytical formulas for the solution of this general class is analytically derived, for consistent and non-consistent initial conditions.Mathematic
Symmetric/skew-symmetric homogeneous matrix descriptor (regular) differential systems with consistent initial conditions
No full textPower series solutions for linear higher order rectangular differential matrix control systems
No full textPower series solutions for linear higher order rectangular differential matrix control systems
No full textThis 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
Investigating the solution properties of symmetric/skew-symmetric LTI homogeneous matrix descriptor discrete-time systems with consistent initial conditions and constant delay period
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