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- W2067265462 abstract "In this paper we study in depth a class of infinite dimensional linear time invariant systems. We get concrete analytic conditions characterizing esact controllability and exact observability in the sense of Helton. Also, we characterize the class of transfer functions having realizations that are exactly controllable and esactly observable. There are currently two approaches to the problem of describing linear systems, using external and internal descriptions. The external description gives the input/output relations, whereas the internal description gives the dynamics of the system that produce the given input/output relations. The problem of realization is to find from a given external description all the possible internal descriptions and the relations among them. This is an impossible task unless some additional assumptions are made. One natural assumption is that in some sense a realization should be minimal. Liehen this assumption is made precise, we get a complete theory for finite dimensional time invariant linear systems, whether discrete or continuous. We will quote some of the highlights of the finite dimensional theory, that will serve as reference and motivation for the results of this paper. For a more complete exposition excellent accounts are in [3, 131. Two linear spaces C.r and 5’ are given. U is called the control space and E’ the output space. A (discrete) linear time invariant input/output map is a linear map sending sequences of elements of U into sequences of elements E such that yrl = Cyzt =jljU,_j_l , where 9j E L( CT, I’). The sequence (A,, -4, ,...) is called the impulse response function, whereas z =l# (or x Aizitl) is called the transfer function of the system. Usually we identify" @default.
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- W2067265462 date "1976-02-01" @default.
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- W2067265462 title "Exact controllability and observability and realization theory in Hilbert space" @default.
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- W2067265462 doi "https://doi.org/10.1016/0022-247x(76)90117-7" @default.
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