On configuration flatness of linear mechanical systems

The concept of differential flatness is an elegant approach to system analysis and the design of controllers and observers. In many cases, however, the main difficulty is the determination of a flat output. For holonomic mechanical systems the notion of “configuration flatness” was introduced some years ago, meaning that a flat output is a function only of configuration variables (and not of the velocities nor the input). Obviously, such a property could drastically facilitate the search for a flat output. In this contribution, we show on the basis of a polynomial matrix representation that for linear conservative mechanical systems left coprimeness (i. e., controllability), which is equivalent to (general) flatness, implies configuration flatness.