Abstract
In 1983, Hautus and Heymann introduced the notion of proper independence to the linear space over the field of rational functions and gave a method for constructing a properly independent basis from the generators of a linear subspace using transformations by polynomial matrix. Using this method, they gave necessary and sufficient conditions for decoupling a injective multivariable linear system by static state feedback.
In this paper, we first propose a method to construct a properly independent basis from the generators of a linear subspace by means of transformations of the generators by bicausal rational matrix. Then, based on this method we show conditions which are equivalent to those of Hautus and Heymann, but which are much simpler to be checked than theirs. In the same time, the new result provides a method to find a decoupling static state feedback.
