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 $HB$, $HAB$, ...

In this paper we present a solution to the decoupling problem with stability of linear multivariable systems with 2 outputs, using nonregular static state feedback. The problem is tackled using an algebraic-polynomial approach, and the main idea is to test the conditions for a decoupling compensator with stability to be feedback realizable. It is shown that the problem has a solution if and only if Morse’s list $I_2$ is greater than or equal to the infinite and unstable structure of the proper and stable...

An upper bound for the complex structured singular value related to a linear time-invariant system over all frequencies is given. It is in the form of the spectral radius of the ${\mathscr{H}}_{\infty }$-norm matrix of SISO input-output channels of the system when uncertainty blocks are SISO. In the case of MIMO uncertainty blocks the upper bound is the $\infty$-norm of a special non-negative matrix derived from ${\mathscr{H}}_{\infty }$-norms of SISO channels of the system. The upper bound is fit into the inequality relation between the results of...