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- W2159151607 abstract "In the first part of the paper we study the pencil $(sE - A)$ by using some geometric concepts given by Bernhard [SIAM J. Control Optim., 20 (1982), pp. 612–6331 and some new ones which are introduced here. Such concepts are then used to obtain an alternative characterization for the finite and infinite-zero structure of the pencil and to construct a polynomial basis for ker $(sE - A)$. Necessary and sufficient conditions for the rows or/and the columns of the pencil to be linearly independent over the ring of the polynomials are also given. The main geometric properties of a regular pencil are presented, including the identification of the subspace in which the impulsive response of the autonomous generalized linear system $Edot x = Ax$ takes place. In the second part we consider the generalized linear system $Edot x = Ax + Bu;y = Cx$ and we give necessary and sufficient conditions for the infinite-zeros of the regular pencil $(sE - A)$ to be controllable and observable." @default.
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- W2159151607 date "1986-07-01" @default.
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- W2159151607 title "The Pencil $(sE - A)$ and Controllability–Observability for Generalized Linear Systems: a Geometric Approach" @default.
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- W2159151607 doi "https://doi.org/10.1137/0324037" @default.
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