I have a series of MIMO LTIs representing the controllers for my MIMO LTI plants, which are the linearization of my nonlinear model. What is the best way to interpolate the controllers to come up with the nonlinear controller?
Interpolating the elements of $A,B,C,D$ representing the controllers seems terribly wrong.
I can interpolate over the output $y$ of each controller according to the scheduling parameter, but I was wondering whether there is a more correct / elegant way that is not a LPV synthesis.
Thanks!
If you would like to interpolate the matrices of a state space model you have to make sure the state associated with each model has a similar meaning. Namely, otherwise you could interpolate similar state space models (with the same frequency response) and get different intermediate frequency responses when interpolating. For example you could use the controllable canonical form for each state space model.
Is is also worth noting that in general interpolating stabilizing controllers, which stabilize the respective linearized system operating point, does not ensure that the nonlinear would be stable.