## Appendix A  
Proof of Theorem 1.: Let \(\mathbf{s}(\overset{\wedge}{\mathbf{x}},\overset{\wedge}{\mathbf{u}}_{k-1})- \mathbf{s}(\overset{\wedge}{\mathbf{x}}_{k},\overset{\wedge}{\mathbf{u}}_{k-1} )=\overset{\wedge}{\mathbf{y}}_{k}-\overset{\vee}{\mathbf{y}}_{k}=\Delta \mathbf{y}_{k}\), where \(\overset{\wedge}{\mathbf{y}}_{k}=\mathbf{s}(\overset{\wedge}{\mathbf{x}}_{k}, \overset{\wedge}{\mathbf{u}}_{k-1}=C(\overset{\wedge}{\mathbf{\xi}}_{k-1}, \overset{\wedge}{\mathbf{\theta}}))\). In VRFT, it is also valid that \(\overset{\wedge}{\mathbf{y}}_{k}=\mathbf{s}(\overset{\wedge}{\mathbf{x}}_{k}, \overset{\wedge}{\mathbf{u}}_{k-1})=\mathbf{s}^{m}(\overset{-m}{\mathbf{x}}_{ k},\overset{\wedge}{\mathbf{\xi}}_{k-1})\) is the output of both the process and of the ORM driven by \(\overset{\wedge}{\mathbf{\tau}}_{k-1}=\mathbf{M}^{-1}(\overset{\wedge}{ \mathbf{y}}_{k})\). By the mean value theorem, there is a \(0<\Gamma<1\) making  
\[\Delta\mathbf{y}_{k}=\frac{\partial\mathbf{s}(\overset{\wedge}{\mathbf{x}}_{k} ^{\Gamma},\overset{\wedge}{\mathbf{u}}_{k-1}^{\Gamma})}{\partial\mathbf{x}_{k} }(\overset{\wedge}{\mathbf{x}}_{k}-\overset{\wedge}{\mathbf{x}}_{k})+\frac{ \partial\mathbf{s}(\overset{\wedge}{\mathbf{x}}_{k}^{\Gamma},\overset{ \wedge}{\mathbf{u}}_{k-1}^{\Gamma})}{\partial\mathbf{u}_{k-1}}(\overset{ \wedge}{\mathbf{u}}_{k-1}-\overset{\wedge}{\mathbf{u}}_{k-1}), \tag{1}\]leading to  
\[\|\Delta\mathbf{y}_{k}\|\leq B_{\mathrm{sx}}\|\Delta\mathbf{x}_{k}\|+B_{\mathrm{s} \mathrm{u}}\|\Delta\mathbf{u}_{k-1}\|, \tag{10}\]  
where \(\mathbf{x}_{k}^{\Gamma}=\Gamma\overset{\wedge}{\mathbf{x}}_{k}+(1-\Gamma) \widetilde{\mathbf{x}}_{k},\mathbf{u}_{k-1}^{\Gamma}=\Gamma\overset{\wedge}{ \mathbf{u}}_{k-1}+(1-\Gamma)\widetilde{\mathbf{u}}_{k-1}\), and \(\Delta\mathbf{x}_{k}=\overset{\wedge}{\mathbf{x}}_{k}-\widetilde{\mathbf{x}} _{k},\Delta\mathbf{u}_{k-1}=\overset{\wedge}{\mathbf{u}}_{k-1}-\widetilde{ \mathbf{u}}_{k-1}\). Observe that (8) implies \(\|\widetilde{\mathbf{u}}_{k}-\mathbf{C}(\overset{\wedge}{\mathbf{x}}_{k}, \overset{\wedge}{\mathbf{\theta}})\|<\varepsilon\), \(\forall k=\overline{0,N-1}\). But \(\Delta\mathbf{u}_{k}=\mathbf{C}(\overset{\wedge}{\mathbf{x}}_{k},\overset{ \wedge}{\mathbf{\theta}})-\widetilde{\mathbf{u}}_{k}=\mathbf{C}(\overset{ \wedge}{\mathbf{x}}_{k},\overset{\wedge}{\mathbf{\theta}})-\mathbf{C}( \overset{\wedge}{\mathbf{x}}_{k}^{E},\overset{\wedge}{\mathbf{\theta}})+ \mathbf{C}(\overset{\wedge}{\mathbf{x}}_{k}^{E},\overset{\wedge}{\mathbf{ \theta}})-\widetilde{\mathbf{u}}_{k}\) and by the MVT there is a \(0<\Gamma<1\) such that  
\[\Delta\mathbf{u}_{k}=\frac{\partial\mathbf{C}(\overset{\wedge}{\mathbf{x}}_{k }^{E\Gamma},\overset{\wedge}{\mathbf{\theta}})}{\partial\overset{\wedge}{ \mathbf{x}}_{k}^{E}}(\overset{\wedge}{\mathbf{x}}_{k}-\widetilde{\mathbf{x}} _{k}^{E})+\mathbf{C}(\overset{\wedge}{\mathbf{x}}_{k}^{E},\overset{\wedge}{ \mathbf{\theta}})-\widetilde{\mathbf{u}}_{k}, \tag{11}\]  
with \(\mathbf{x}_{k}^{E\Gamma}=\Gamma\overset{\wedge}{\mathbf{x}}_{k}^{E}+(1-\Gamma )\widetilde{\mathbf{x}}_{k}^{E}\), leading to  
\[\|\Delta\mathbf{u}_{k}\|\leq B_{\mathrm{c}\mathrm{x}}\|\Delta\mathbf{x}_{k}^{ E}\|+\varepsilon, \tag{12}\]  
for \(\Delta\mathbf{x}_{k}^{E}=\overset{\wedge}{\mathbf{x}}_{k}^{E}-\overset{ \wedge}{\mathbf{x}}_{k}^{E}\). But \(\Delta\mathbf{x}_{k}^{E}=\overset{\wedge}{\mathbf{x}}_{k}^{E}-\overset{ \wedge}{\mathbf{x}}_{k}^{E}=[ \begin{pmatrix}\overset{\wedge}{\mathbf{x}}_{k}- \widetilde{\mathbf{x}}_{k}^{E}\\ \end{pmatrix}