Journal of Applied Mathematics

Controllability and Observability Criteria for Linear Piecewise Constant Impulsive Systems

Hong Shi and Guangming Xie

Full-text: Open access

Abstract

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.

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 182040, 24 pages.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1355495278

Digital Object Identifier
doi:10.1155/2012/182040

Mathematical Reviews number (MathSciNet)
MR2965714

Zentralblatt MATH identifier
1251.93038

Citation

Shi, Hong; Xie, Guangming. Controllability and Observability Criteria for Linear Piecewise Constant Impulsive Systems. J. Appl. Math. 2012 (2012), Article ID 182040, 24 pages. doi:10.1155/2012/182040. https://projecteuclid.org/euclid.jam/1355495278


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