Electrical – FOC Induction Motor Control – Rotor Flux Angle

Induction motors have an even number of poles or any number of pole pairs formed on the stator by the winding pattern. The stator field induces currents in the rotor that form a matching number of poles on the rotor.

I agree that using the \$\omega_m\$ to produce a time-varying observer is a valid and intuitive approach. The "theoretical correctness" of it will mostly depend on two aspects, and both will require some reading and research on your part.

(1) the criterias you want to guarantee for the closed-loop system. This mostly concerns stability guarantees and perhaps some pole-placement objectives.

(2) the design method you will be using (i.e. how the gain coefficients of closed loop are obtained).

My suggestion is that you start by modeling \$\omega_m\$ as an uncertain parameter within \$\omega_{min}\$ and \$\omega_{max}\$, so now your system is "bounded by a polytope". This will produce LMI (linear matrix inequality) constraints that can be used to guarantee quadratic stability of the system. Such constraints can also easily be coupled with \$H_2\$ or \$H_\infty\$ design objectives to produce a convex optimization problem. There are plenty of papers available on the topic if you search using these keywords. Good luck!

Additional question in comments: eigenvalues of the above mentioned system matrix in symbolic form?

You can always use a symbolic calculator to figure this out. Just did it using WolframAplha:

Just replace \$a=-\alpha\$, \$b=\beta\$, \$c=\gamma\omega_m\$, \$d=R_r\frac{L_h}{L_r}\$, \$e=-\frac{R_r}{L_r}\$ and \$f=-\omega_m\$