For control of cascaded linearized system, my objective is to design a stabilizing controller. For stability and performance analysis of such structures, I have been trying to find a book where such problems, even at a much simplified level, are treated but failed to do so. I read through one of the questions already asked (Asymptotic stability of cascade control) but the approaches described are, let's say, not so relevant in my case, since for my linearized system, I do not need the Lyapunov approach to investigate stability. Although I would want to prove it for the complete nonlinear system rather than the linearized system. Any reference to a book that can give insights into the control of general cascaded systems (including nonlinear) would be appreciated.
I think it may help to find out what prompted me to ask this question. As discussed my objective is to stabilize a system for which I decided to adopt a cascaded approach i.e. I divide my system into two loops - inner and outer. Since the system pertains to a vehicle, the outer controller performs the path planning and generates set point for the inner controller which performs the steering control on the vehicle. Since its a linear system, I write the state-space of the entire cascaded system which is controllable and hence get a static state feedback ensuring asymptotic stability. The problem is this does not translate in simulation.
Note that the controllers are not individually designed. Using the property of controllability which both loops have, I assume a static state feedback for both loops and assign them values only based on the stability requirements of the complete cascaded system. Its hard to figure out what went wrong!
Let me know if more information is required.
The image is a general overview to understand what I mean by a cascaded structure.
Note: The position of the block $E$ may vary!