Controllability and Observability Criteria for Linear Piecewise Constant Impulsive Systems
Impulsive differential systems are an important class of mathematical models for many practical systems in physics, chemistry, biology, engineering, and information science that exhibit impulsive dynamical behaviors due to abrupt changes at certain instants during the dynamical processes. This paper...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/182040 |
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| author | Hong Shi Guangming Xie |
| author_facet | Hong Shi Guangming Xie |
| author_sort | Hong Shi |
| collection | DOAJ |
| description | Impulsive differential systems are an important class of mathematical models for many practical systems in physics, chemistry, biology, engineering, and information science that exhibit impulsive dynamical behaviors due to abrupt changes at certain instants during the dynamical processes. This paper studies the controllability and observability of linear piecewise constant impulsive systems. Necessary and sufficient criteria for reachability and controllability are established, respectively. It is proved that the reachability is equivalent to the controllability under some mild conditions. Then, necessary and sufficient criteria for observability and determinability of such systems are established, respectively. It is also proved that the observability is equivalent to the determinability under some mild conditions. Our criteria are of the geometric type, and they can be transformed into algebraic type conveniently. Finally, a numerical example is given to illustrate the utility of our criteria. |
| format | Article |
| id | doaj-art-146ad03c77074655a04e308717c253b4 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-146ad03c77074655a04e308717c253b42025-02-03T01:13:12ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/182040182040Controllability and Observability Criteria for Linear Piecewise Constant Impulsive SystemsHong Shi0Guangming Xie1Mathematics and Physics Department, Beijing Institute of Petrochemical Technology, Beijing 102617, ChinaCenter for Systems and Control, LTCS, and Department of Industrial Engineering and Management, Peking University, Beijing 100871, ChinaImpulsive differential systems are an important class of mathematical models for many practical systems in physics, chemistry, biology, engineering, and information science that exhibit impulsive dynamical behaviors due to abrupt changes at certain instants during the dynamical processes. This paper studies the controllability and observability of linear piecewise constant impulsive systems. Necessary and sufficient criteria for reachability and controllability are established, respectively. It is proved that the reachability is equivalent to the controllability under some mild conditions. Then, necessary and sufficient criteria for observability and determinability of such systems are established, respectively. It is also proved that the observability is equivalent to the determinability under some mild conditions. Our criteria are of the geometric type, and they can be transformed into algebraic type conveniently. Finally, a numerical example is given to illustrate the utility of our criteria.http://dx.doi.org/10.1155/2012/182040 |
| spellingShingle | Hong Shi Guangming Xie Controllability and Observability Criteria for Linear Piecewise Constant Impulsive Systems Journal of Applied Mathematics |
| title | Controllability and Observability Criteria for Linear Piecewise Constant Impulsive Systems |
| title_full | Controllability and Observability Criteria for Linear Piecewise Constant Impulsive Systems |
| title_fullStr | Controllability and Observability Criteria for Linear Piecewise Constant Impulsive Systems |
| title_full_unstemmed | Controllability and Observability Criteria for Linear Piecewise Constant Impulsive Systems |
| title_short | Controllability and Observability Criteria for Linear Piecewise Constant Impulsive Systems |
| title_sort | controllability and observability criteria for linear piecewise constant impulsive systems |
| url | http://dx.doi.org/10.1155/2012/182040 |
| work_keys_str_mv | AT hongshi controllabilityandobservabilitycriteriaforlinearpiecewiseconstantimpulsivesystems AT guangmingxie controllabilityandobservabilitycriteriaforlinearpiecewiseconstantimpulsivesystems |