A new form of the coprime polynomial fraction $C\left(s\right)F{\left(s\right)}^{-1}$ of a transfer function matrix $G\left(s\right)$ is presented where the polynomial matrices $C\left(s\right)$ and $F\left(s\right)$ have the form of a matrix (or generalized matrix) polynomials with the structure defined directly by the controllability characteristics of a state- space model and Markov matrices $HB$, $HAB$, ...

The problem of diagnostic filter design is studied. Algebraic and geometric approaches to solving this problem are investigated. Some relations between these approaches are established. New definitions of fault detectability and isolability are formulated. On the basis of these definitions, a procedure for diagnostic filter design is given in both algebraic and geometric terms.

Numerical operations on and among rational matrices are traditionally handled by direct manipulation with their scalar entries. A new numerically attractive alternative is proposed here that is based on rational matrix interpolation. The procedure begins with evaluation of rational matrices in several complex points. Then all the required operations are performed consecutively on constant matrices corresponding to each particular point. Finally, the resulting rational matrix is recovered from the...