Observer-based pole placement for non-lexicographically-fixed linear time-varying systems

In this paper, the observer based pole placement control for non-lexicographically-fixed linear time-varying MIMO systems is considered. Using the concept of the relative degrees of a MIMO system, Ackerman-like design algorithm for pole placement state feedback control is directly derived. This makes the calculation procedure to obtain the pole placement state feedback very simple, especially for MIMO systems. The separation principle is also shown in the case where both of the controllability indices and the observability indices are not lexicographically-fixed.