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

Abstract EN

Nowadays, quantum systems have become one of the focuses of the ongoing research and theyare 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 oncomplex field, for simplicity, complex linear impulsive systems.

This kind of time-driven impulsivesystems allows free impulsive instants, which leads to the limitation of using traditional definitions ofreachability and observability directly.

New notations about the span reachable set and unobservableset are proposed.

Sufficient and necessary conditions for span reachability and observability of suchsystems are established.

Moreover, the explicit characterization of span reachable set and unobservableset is presented by geometric analysis.

It is pointed out that the geometric conditions are equivalent tothe algebraic ones in known results for special cases.

Numerical examples are also presented to showthe effectiveness of the proposed methods.