Looking for RIGOROUS and Proof-based course on Control theory.
Hi everyone,
I followed multiple course on control theory : i know how to analyse a linear system, to derive PID controllers / RST controllers and H-infinty based controller. I understand how it works in practice and i have a good intuition for it.
However, i lack the underlying mathematical framework (and also Lyapunov theory) supporting the whole field. What function space are we working in ? In under which condition the stability of the linearised system at some point guarantees the stability of the whole systems etc...
I have seen the proof of the Kalman theorem but where i saw it, it was cutting corner and relies on the construction on an explicit control and base decomposition in a finite hilbert space (What about control in infinite dimensional spaces ??? Is there a K-theorem equivalent)
And honestly, i only found text books either practice-oriented (ewww) or more mathematical textbook but with AWFUL NOTATIONS.
Do you know about a well-written, proof-based course on control (w/o "handwaving" and reference to this or that) and with decent notations ?
Sorry for ranting but i think control theory is beautiful but i only get accross the same copy-pasted shit engineer oriented control textbooks.
Thank you for reading and have a good day !