Rational function matrices and structural controllability and observability

A matrix is said to be a rational function matrix (RFM) if each entry in the matrix is a rational function of independent parameters with real coefficients. A linear time-invariant system is said to be a rational function system (RFS) if each of its coefficient matrices is a RFM. The Lebesque measure of the set of points in the parameter space of a RFS is introduced to define structural controllability and observability (SC-SO) of the RFS. Some criteria for SC-SO of the RFS are proven and some illustrative examples given