Deformation and stability of triples of matrices
For a linear dynamical system described by \(\dot x= Ax+Bu\), \(y=Cx\), \(x\in\mathbb{C}^n\), \(u\in\mathbb{C}^m\), \(y\in \mathbb{C}^p\), based on a result describing explicitly the orthogonal miniversal deformation of \((A,B,C)\), one shows that the structural stability of \((A,B,C)\) is equivalent with one of the following conditions, corresponding to a different relation among \(n\), \(m\) and \(p\): (a) \(n\leq \min(m,p):(A,B,C)\) has only infinite elementary divisors with exponent two. (b) \(m>p\), \(n\geq p\); \((A,B,C)\) has only column-minimal indices that are equal or differ by one unity, and infinitely many elementary divisors with exponent two. (c) \(p>m\), \(n\geq m:(A,B,C)\) has only row-minimal indices that are equal or differ by one unity, and infinitely many elementary divisors with exponent two.
scientific article; zbMATH DE number 1000051