Controllability and observability for linear quaternion-valued impulsive differential equations

Abstract

In this paper, the controllability and observability for linear quaternion-valued impulsive differential equations (QIDEs) are investigated. We mainly establish some sufficient and necessary conditions for state controllability and state observability of linear QIDEs. By virtue of the isomorphism between quaternion vector space and complex variables space as well as the adjoint matrix of quaternion matrix, all the theoretical results in the sense of complex-valued and quaternion-valued are equivalent to each other. Finally, the validity of theoretical results acquired is indicated by two instances shown.