Abstract
The problem is considered in this paper of finding the minimal order inverse system of a multivariable time-invariant linear dynamical system under the condition that the allowable number of ideal differentiators required in the inversion is specified. It is first shown that such inversion problem can be reduced to the problem of designing the linear function observer for an associated dynamical system. The minimal order of the inverse system for the multivariable case is uniquely determined by noting that it is essentially equivalent to the minimal order of the observer. Then the stability of the minimal order inverse system is carefully investigated, and it is also shown that the stable lower order inverse system can be readily constructed with the aid of the reduced order state observer design. Finally the minimal number of output differentiations required to realize the exact minimal order inverse system is given.
