Efficient eigenvalue assignments for general linear MIMO systems
Automatica (Journal of IFAC)
Linear System Theory and Design
Linear System Theory and Design
| Hi-index | 22.15 |
This document is the third in a series of recent eigenvalue placement studies by the authors. In the first two publications (Valasek and Olgac, 1995a, Automatica, 31(11) 1605-1617 and 1995b IEE Control Theory Appl. Proc 142 (5), 451-458) the extension of Ackermann's formula to time varying SISO and later to time-invariant and -varying MIMO systems were presented. Pole placement for linear time-varying systems means that the closed-loop system is equivalent via a Lyapunov transformation to a linear time-invariant system with poles at prescribed locations. In addition to the controllability condition, a critical property in this process is lexicographically fixedness, which was taken as granted at all times in the prior work. In this paper we deal with the pole placement of linear time-varying MIMO systems which are not lexicographically fixed. This effort removes the last restriction in the pole placement of such systems aside from being controllable. The original linear time-varying MIMO system which is not lexicographically fixed is augmented by appending additional state equations to ensure that the embedded system has the property of lexicographically fixedness. The poles are then placed as desired for this augmented system using the techniques presented in our previous publications. There is an added work of placing also the extra poles which appear due to the augmentation. However, they can be selected sufficiently away from the originally intended poles so that they do not influence the system behavior. Examples are provided to validate this claim.