I have following dynamic system
$$ \frac{\mathrm{d}v_C}{\mathrm{d}t} = -\frac{1}{R_b\cdot C}\cdot v_C\cdot\alpha, $$
where $v_C$ is the system state and output, $\alpha$ is the system input and $R_b, C$ are the system parameters. Due to the fact that the differential equation contains product of the state and input variable the system is non-linear. For the PI controller design it will be necessary to linearize the system in a given steady state operating point $(v_{C_{0}}, \alpha_0)$.
I have done this linearization
$$ \frac{\mathrm{d}\widetilde{v_C}}{\mathrm{d}t} = -\frac{1}{R_b\cdot C}\left(v_{C_{0}}\cdot\widetilde{\alpha} + \widetilde{v_C}\cdot\alpha_0\right), $$
where $\widetilde{\alpha}$ and $\widetilde{v_{C}}$ are the perturbations from the steady state operating point. This linearized model can be transformed into the Laplace domain
$$ \frac{\widetilde{V}_C(s)}{\widetilde{\alpha}(s)} = -\frac{\frac{v_{C_{0}}}{R_b\cdot C}}{s + \frac{\alpha_0}{R_b\cdot C}} $$
Here the PI controller design can be started but the transfer function is strongly dependent on the selection of the steady state operating point. My question is how to proceed in such situation? What steady state operating point shall I select for the PI controller design?