Behavior for Time Invariant Finite Dimensional Discrete Linear Systems

Sisilia Sylviani, Hanni Garminia & Pudji Astuti
Algebra Research Group,  Faculty of Mathematics and Natural Sciences
Institut Teknologi Bandung, Jalan Ganesa 10, Bandung 40132, Indonesia
Email: pudji@math.itb.ac.id

Abstract. The behavior of a dynamical system, in Willems’s point of view, is the set of all trajectories of the system. Fuhrmann defines a behavior as a linear, shift invariant, and complete subspace of z^-1F^m[[z^-1]], the vector space consisting of power series in z^-1 with coefficients in signal space W=F^m. In this paper we show that the behavior of a finite dimensional, time invariant discrete linear system in Willems’s setting is also a behavior according to Fuhrmann’s. 

Keywords: behavior; complete; linear system; shift invariant; trajectories.