I was reading about designing of controller by state state model from book by Norman S. Nise
And author suggested that if state space representations given in problem are of form other than phase variable form then best method to design a controller would be
1.transform given system to phase variable form
2.then design the feedback gains
3.then again transform the designed system back to original state space form
So my question
1.when we transform from one of state space representations to another , isn't zeroes of system may changed?
Or in other words
isn't transfer function gets changed due to transformation
As I try to figure out myself here is my attempt
And after all this calculation to me it seems that both transfer function may not be equal always
example given in book shows that it has same transfer function in both transforms so I thought it(example) may be a special case
So can anyone explain
Mathematical expression I got can be solved further to obtain a relationship between both transfer function ?
my conclusion is right that transfer function may or may not changed due to transformation?