Transferring Instantly the State of Higher-Order Linear Descriptor (Regular) Differential Systems Using Impulsive Inputs
In 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 D...
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | Journal of Control Science and Engineering |
| Online Access: | http://dx.doi.org/10.1155/2009/562484 |
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| author | Athanasios D. Karageorgos Athanasios A. Pantelous Grigoris I. Kalogeropoulos |
| author_facet | Athanasios D. Karageorgos Athanasios A. Pantelous Grigoris I. Kalogeropoulos |
| author_sort | Athanasios D. Karageorgos |
| collection | DOAJ |
| description | In 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. |
| format | Article |
| id | doaj-art-b8addc450d554f23b8399e1c1522fc01 |
| institution | DOAJ |
| issn | 1687-5249 1687-5257 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Control Science and Engineering |
| spelling | doaj-art-b8addc450d554f23b8399e1c1522fc012025-08-20T03:22:50ZengWileyJournal of Control Science and Engineering1687-52491687-52572009-01-01200910.1155/2009/562484562484Transferring Instantly the State of Higher-Order Linear Descriptor (Regular) Differential Systems Using Impulsive InputsAthanasios D. Karageorgos0Athanasios A. Pantelous1Grigoris I. Kalogeropoulos2Department of Mathematics, University of Athens, Athens, GreeceDepartment of Mathematics, University of Athens, Athens, GreeceDepartment of Mathematics, University of Athens, Athens, GreeceIn 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.http://dx.doi.org/10.1155/2009/562484 |
| spellingShingle | Athanasios D. Karageorgos Athanasios A. Pantelous Grigoris I. Kalogeropoulos Transferring Instantly the State of Higher-Order Linear Descriptor (Regular) Differential Systems Using Impulsive Inputs Journal of Control Science and Engineering |
| title | Transferring Instantly the State of Higher-Order Linear Descriptor (Regular) Differential Systems Using Impulsive Inputs |
| title_full | Transferring Instantly the State of Higher-Order Linear Descriptor (Regular) Differential Systems Using Impulsive Inputs |
| title_fullStr | Transferring Instantly the State of Higher-Order Linear Descriptor (Regular) Differential Systems Using Impulsive Inputs |
| title_full_unstemmed | Transferring Instantly the State of Higher-Order Linear Descriptor (Regular) Differential Systems Using Impulsive Inputs |
| title_short | Transferring Instantly the State of Higher-Order Linear Descriptor (Regular) Differential Systems Using Impulsive Inputs |
| title_sort | transferring instantly the state of higher order linear descriptor regular differential systems using impulsive inputs |
| url | http://dx.doi.org/10.1155/2009/562484 |
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