Behavior for Time Invariant Finite Dimensional Discrete Linear Systems

Sisilia Sylviani, Hanni Garminia, Pudji Astuti

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-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.

Keywords


behavior; complete; linear system; shift invariant; trajectories

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References


Willems, J.C., The Behavioral Approach to Open and Interconnected Systems, IEEE Control Systems Magazine, 27(6), pp. 46-99, 2007.

Willems, J.C., From Time Series to Linear Systems. Part I: Finite-Dimensional Linear Time Invariant Systems, Automatica, 22(5), pp. 561-580, 1986.

Fuhrmann, P.A., A Study of Behavior, Linear Algebra and Its Applications, 351-352, pp. 303-380, 2002.

Fuhrmann, P.A., Linear Systems and Operators in Hilbert Space, McGraw-Hill, New York, 19813.




DOI: http://dx.doi.org/10.5614%2Fj.math.fund.sci.2013.45.1.4

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