The paper develops an idea of specification of stability for a
perturbed linear difference Cauchy problem which is singular but
which is still tractable (i.e., regularized) via suitable
projection operators. Such a Cauchy problem is called ``implicit"
and it may be perceived as equivalent to a combination of an
ordinary difference system and an algebraic relation. What is
addressed in the paper is the characterization of stability of the
solutions under a specific (so called causal) class of
perturbations. Their strength is measured by the so called
stability radius, real or complex. The formula for its computation
is the main result of the paper. Recommended introductory reading:
ten years old reference [7] (where the system under consideration
has been differential and explicit, non-singular).
MR2513049 Rodjanadid, Benjawan; Nguyen, Van Sanh; Nguyen, Thu Ha;
Nguyen, Huu Du Stability radii for implicit difference equations.
Asian-Eur. J. Math. 2 (2009), no. 1, 95--115. 65Q05 (34D20 93C55
93D05)