\end{aligned}$$ with $S(-B^*,A^*)$ being the Sylvester matrix associated with the polynomials $-B^*(p)$ and $A^*(p)$, which is non-singular since $A^*(p)$ and $B^*(p)$ are coprime. Hence, we can write the expected value of interest as $$\begin{aligned}
    \overline{E}\{\hat{\varphi}_f(t_k)\varphi_f^\top(t_k)\} &= S(-B_j,A_j)\Phi_1 S^\top(-B^*,A^*) \notag \\
    \label{righthandside}
    &\hspace{-1.9cm}+S(-B_j,A_j)\overline{E}\left\{\left[ \dfrac{U_{du}(t)}{A_j^2(p)} \right]_{t_k}\Delta^\top(t_k)\right\},
    \end{aligned}$$ where $$\Phi_1 := \overline{E}\left\{ \left[\frac{U_{du}(t)}{A_j^2(p)}\right]_{t_k} \left[\frac{U_{du}(t)}{A_j(p)A^*(p)} \right]_{t_k}^\top \right\}. \notag$$ It is shown in Lemma \[lemma2\] that $\Phi_1$ is generically non-singular, which means that the first summand of the right hand side of is generically non-singular.

Finally, as $h$ tends to zero, the infinity norm of the difference between the direct evaluation of a CT signal and its interpolated counterpart also tends to zero. Thus, $\Delta(t_k)\to 0$ as $h\to 0$. This, together with the fact that (generic) non-singularity of a matrix is preserved under small-enough matrix perturbations [@Horn2012 Chap. 6], leads to the first statement of the theorem.

*Statement 2*. Suppose that $\bar{\theta}$ is a limiting point of the iteration in , where $\varphi_f(t_k)$ and $\hat{\varphi}_f(t_k)$ are defined as in  and respectively, and the corresponding polynomials are denoted by $\bar{A}(p)$ and $\bar{B}(p)$. These polynomials are coprime by Assumption \[assumption4\]. The ergodic lemmas in [@soderstrom1975ergodicity Lemma 3.1] and [@soderstrom1983instrumental Lemma A4.3] permit us to write the iteration 