Description linearized tanks

Question

Description linearized tanks I have a task to complete with the following content: Given a system of two conical tanks connected in a cascade, H1=15m , D1=5m, H2=10m, D2=7m and the free outflow is specified $ F_{iwy}=\alpha_i \sqrt{h_i} $ (h is current water level in n-tank) with the maximum values of these outflows being equal to respectively $F_{1wy_{max}} = 0.02\text{ mm}^3/\text{s} $ and $F_{2wy_{max}} = 0.015\text{ m}^3/\text{s}$ .Find the linearized description $\begin{align*}X &= AX+BU\end{align*}$ $\begin{align*}Y&=CX + DU\end{align*}$ selecting as state variables the instantaneous values of h1 and h2, y=F2wy and control F1 with initial state H10 = 10m and H20 corresponding to stable operating point(h10,h20,F2wy0). I know that in order to find a linearized description, I need to create the equations of state for the system and determine the matrix. My idea for the matrix is as follows: $\frac{d}{dt} h_{10}$ $\frac{d}{dt} h_{20}$ $\frac{d}{dt} F_{2wy0}$ Could I ask for a hint if I am thinking correctly with this matrix? If so, how do I determine the various equations in it? Thank you in advance for any guidance. Sketch of tanks