Abstract
The objective of this paper is to make clear the fundamental importance of thefundamental matrix ϕ k in the analysis of linear discrete-time singular systems. We relateϕ k to the coefficientsR k of the adjoint matrix (zE-A)−1, find an autoregressive recursion for theϕ k , and give the solution of the singular semistate equation in terms ofϕ k . Also discussed are thesemistatetransition matrix and the singular systemTschirnhausen polynomials. We close by giving a stable numerical technique for the computation of the sequenceϕ k that is based on first taking the pencilzE-A to triangular form.
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