Behavior for Time Invariant Finite Dimensional Discrete Linear Systems
Keywords:behavior, complete, linear system, shift invariant, trajectories
AbstractThe behavior of a dynamical system, in Willemsâ€™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 Willemsâ€™s setting is also a behavior according to Fuhrmannâ€™s.
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