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2012 Controllability and Observability Criteria for Linear Piecewise Constant Impulsive Systems
Hong Shi, Guangming Xie
J. Appl. Math. 2012: 1-24 (2012). DOI: 10.1155/2012/182040


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.


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Hong Shi. Guangming Xie. "Controllability and Observability Criteria for Linear Piecewise Constant Impulsive Systems." J. Appl. Math. 2012 1 - 24, 2012.


Published: 2012
First available in Project Euclid: 14 December 2012

zbMATH: 1251.93038
MathSciNet: MR2965714
Digital Object Identifier: 10.1155/2012/182040

Rights: Copyright © 2012 Hindawi


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