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The finite precision stability of a discrete-time system realized in companion form is shown to be closely connected to a positive real character of a related all-pole-minus-one-half transfer function. This is shown as a consequence of some novel characterizations of solutions to a Lyapunov equation for companion matrices. The results are of practical significance as companion matrix state recursions are cheap to implement.>
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P.A. Regalia (1992) studied this question.
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