Abstract
Previously the author showed a case where the maximal amplitude of the response of a closed loop regulator becomes extremely large as the ploes approach infinity in the left half complex plane.
This paper, explains this fact by the theory of linear structure of systems.
Namely if the regulator is given by, x=(A+bf)x and y=cx, only for the initial state x(0)∈ν, the maximal amplitude of y increases infinitely as all poles are assigned negative infinity by f. Where ν=span(b, Ab, …, An-m-1b), n. is the dimension of x and m is the number of the zeros of the transfer function c(sI-A)-1b.
The duality of this result provides clear explanation for the similar case given by Bongiorno et al. in the design of an observer.
