Real Radius of Controllability for Systems Described by Polynomial Matrices: SIMO case

In this paper we discuss the problem of computing the real radius of controllability of the Single Input Multi Output (SIMO) systems described by univariate polynomial matrices. The problem is equivalent to computing the nearest noncoprime polynomial matrix to the polynomial matrix describing the system in some prescribed norm. A particular case of this problem is to compute approximate GCD of univariate polynomials. Further this problem is shown to be equivalent to the Structured Low Rank Approximation (SLRA) of a linearly structured resultant matrix associated with the given polynomial matrix. The radius of controllability is then computed by finding the nearest SLRA of this resultant matrix.