On The Loop Transfer Recovery

This paper provides a further theoretical analysis of an entirely new approach to the problem of loop transfer recovery (LTR). This approach is to minimize the observer gain to the system input by observer pole selection. This paper proves that this new approach aims directly at achieving the necessary and sufficient condition of LTR. This paper also proves that this approach guarantees the observer stability for non-minimum phase systems and is applicable for all different types of observers. An analytical and approximate solution with finite observer gain has been derived from this approach. Although in general a finite observer gain cannot achieve precise LTR (so does this solution), only finite observer gain is technically acceptable and physically realizable. For the complete description of this approach, its dual version is also presented in this paper.