Algorithm 1: Algorithm for setting the parameters of the observer (3)–(5).
Step	Description
1	Cast the system model in the form (1)–(2) and identify the known state $x_1$, the unknown state $x_2$, and the terms $b$, $h_1$,$h_2$, ${\delta }_1$, ${\delta }_2$.
2	Obtain the values of $b_{min}$ that satisfy Assumption 2 and the values of $d_2$, $d_1$, satisfying Equation (18). To this end, the values of $d_2$, $d_1$ can be obtained by the simulation of ${\delta }_2/b$,${\delta }_1/b$, based on the $x_1$, $x_2$ model, with model parameter values obtained from either closely related studies or offline fitting.
3	Set the values of $\omega$, $\epsilon$ to define: −The time-dependent bound for the transient evolution of ${\overline{x}}_2$, given by Equation (15):$\left|{\overline{x}}_2\right|\le \left|{\psi }_{zo}\right|e^{-\omega b_{min}\left(t-t_o\right)}+max\left\{-{\delta }_{min},{\delta }_{max}\right\}+\omega \epsilon ; for t\ge T_1$ −The limit of the convergence region of ${\overline{x}}_2$, given by Equations (19) and (20): ${\Omega }_{x2}=\left\{{\overline{x}}_2:\left|{\overline{x}}_2\right|\le f_w \right\}$; $f_w=\frac{1}{\omega }{d}_2+d_1+\omega \epsilon$ where $f_w>d_1\ge \underset{t\ge t_o}{\sup } \left|{\delta }_1/b\right|$ and the minimum point of $f_w$ is given by Equation (22): ${\omega }^{*}=\sqrt{d_2}\frac{1}{\sqrt{\epsilon }}$; $f_w^{*}=2\sqrt{d_2}\sqrt{\epsilon }+d_1$
4	Set a high value of $\gamma$ to define the update rate of $\widehat{\theta }$, according to Equation (5). Set a high value of $k$ to define the convergence rate of ${\overline{x}}_1$, according to Equation (11).