Deadbeat control : a special inverse eigenvalue problem

Van Dooren, Paul
(1984) Bit (Lisse) : numerical mathematics — Vol. 24, p. 681-699 (1984)

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  • Van Dooren, PaulUCLouvain
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Abstract
In this paper we give a numerical method to construct a rank m correction BF (where the n x m matrix B is known and the m x n matrix F is to be found) to a n x n matrix A, in order to put all the eigenvalues of A +BF at zero. This problem is known in the control literature as "deadbeat control". Our method constructs, in a recursive manner, a unitary transformation yielding a coordinate system in which the matrix F is computed by merely solving a set of linear equations. Moreover, in this coordinate system one easily constructs the minimum norm solution to the problem. The coordinate system is related to the Krylov sequence A(-1)B, A(-2)B, A(-3)B,.... Partial results of numerical stability are also obtained.
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Van Dooren, P. (1984). Deadbeat control : a special inverse eigenvalue problem. Bit (Lisse) : numerical mathematics, 24, 681-699. https://doi.org/10.1007/BF01934924 (Original work published 1984)