I ask the advice of specialists on control systems. We have the following system.
Where $u(t)$ and $y(t)$ time-varying input and output. The characteristic $y(t)=f(u(t))$ is assumed to be non-inertial.
Only input and output are available for measurement.
Let me make a reservation that the variant of estimating this derivative by the Euler method, i.e.
$g(t)=\frac{y_{n}(t)-y_{n-1}(t)}{u_{n}(t)-u_{n-1}(t)}$
is not suitable, since the system does not allow elements of delays (delay by 1 time step).
Is it possible to construct an observer estimating the gradient $g(t)=\frac{dy}{du}$?