Journal of Applied Mathematics

Geometric Analysis of Reachability and Observability for Impulsive Systems on Complex Field

Shouwei Zhao, Jitao Sun, and Hai Lin

Full-text: Open access

Abstract

Nowadays, quantum systems have become one of the focuses of the ongoing research and they are typical complex systems, whose state variables are defined on the complex field. In this paper, the issue of reachability and observability is addressed for a class of linear impulsive systems on complex field, for simplicity, complex linear impulsive systems. This kind of time-driven impulsive systems allows free impulsive instants, which leads to the limitation of using traditional definitions of reachability and observability directly. New notations about the span reachable set and unobservable set are proposed. Sufficient and necessary conditions for span reachability and observability of such systems are established. Moreover, the explicit characterization of span reachable set and unobservable set is presented by geometric analysis. It is pointed out that the geometric conditions are equivalent to the algebraic ones in known results for special cases. Numerical examples are also presented to show the effectiveness of the proposed methods.

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 876120, 12 pages.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1355495043

Digital Object Identifier
doi:10.1155/2012/876120

Mathematical Reviews number (MathSciNet)
MR2880850

Zentralblatt MATH identifier
1243.34093

Citation

Zhao, Shouwei; Sun, Jitao; Lin, Hai. Geometric Analysis of Reachability and Observability for Impulsive Systems on Complex Field. J. Appl. Math. 2012 (2012), Article ID 876120, 12 pages. doi:10.1155/2012/876120. https://projecteuclid.org/euclid.jam/1355495043


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