Long-term behavior of cross-dimensional linear dynamical systems

• Let M and V denote the sets of finite-dimensional matrices and finite-dimensional column vectors, respectively. Based on the semitensor product and the vector addition, M and V both form a monoid, where V is commutative. In addition, based on an equivalence relation. on V, the induced quotient space V/<-> forms a vector space. In this paper, we give a basis for the vector space V/<->, showing that V/<-> is of countably infinite dimension. In addition, we give an explicit characterization for how the dimension of a vector in V changes caused by the repetitive actions of a matrix in M on the vector, and characterize the generalized inverse behavior of the repetitive actions.

Ämnesord

TEKNIK OCH TEKNOLOGIER  -- Elektroteknik och elektronik -- Reglerteknik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Electrical Engineering, Electronic Engineering, Information Engineering -- Control Engineering (hsv//eng)

Nyckelord

Long-term behavior

cross-dimensional vector space

cross-dimensional linear dynamical system

dimension-boundedness

basis

Drazin inverse

Publikations- och innehållstyp

ref (ämneskategori)

kon (ämneskategori)