A new approach to the state-transfer problem

A new and simple solution to the problem of determining a function which will effect a possible state transfer of a linear, time-invariant system is presented here. This solution is based on relating the given system to a family of phase-variable canonical form systems, i.e. to a family of scalar differential equations, and solving the problem for the latter by two-point interpolation. It applies to uncontrollable as well as controllable systems; the required control function is not restricted to the class of polynomials; and no computation of the state-transition matrix is involved.