Inversion of multivariable linear systems

Abstract

A new algorithm for constructing an inverse of a multivariable linear dynamical system is presented. This algorithm, which is considerably more efficient than previous methods, also incorporates a relatively simple criterion for determining if an inverse system exists. New insight into the structure of a system inverse is gained by consideration of the inverse system representations resulting from the algorithm. A precise bound on the number of output differentiations required is obtained as well as a bound on the total number of integrators and differentiators necessary to realize the inverse. This latter bound is equal to the order of the original system. A further advantage of the algorithm and theory developed is that it is applicable to both time-invariant systems and time-variable systems which satisfy certain regularity conditions. One application is also given: a complete description of the set of initial states necessary and sufficient for a specified function to be the output of an invertible system.