Behavior for Time Invariant Finite Dimensional Discrete Linear Systems

Sisilia Sylviani (Algebra Research Group, Faculty of Mathematics and Natural Sciences Institut Teknologi Bandung)
Hanni Garminia (Algebra Research Group, Faculty of Mathematics and Natural Sciences Institut Teknologi Bandung)
Pudji Astuti (Algebra Research Group, Faculty of Mathematics and Natural Sciences Institut Teknologi Bandung)

Journal of Mathematical and Fundamental Sciences
Vol. 45 No. 1 (2013)

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-1Fm[[z-1]], the vector space consisting of power series in z-1 with coefficients in signal space W=Fm. 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.