Abstract
This paper proposes a new type inverse, which is dynamical (that is, without pure differentiators) and stable, for linear time-invariant continuous-time systems. Most of the inverses considered in previous studies can be classified into two types:
Type 1; inverses which reproduce the input to the original systems by using differentiators.
Type 2; inverses which reproduce the integral value of the input without using differentiators.
But in type 1, the use of differentiators are not desirable from practical point of view. As for the inverses of type 2, from the knowledge of the integral value of input we cannot know the real value of input without differentiation. In addition to that, inverses of type 2 are generally unstable as shown later in this paper. So we propose a new type inverse called filtered inverse which is dynamical, reproduces the approximate value of the input, and can be realized as a stable system.
The definition and existence condition of the filtered inverse are given first. Then the stability and minimal realization of this inverse are considered. The stability of usual inverses are also considered to show the necessity of filtered inverses. Finally application of the filtered inverse to servo systems and a numerical example are presented.
