Stratification of linear systems. Bifurcation diagrams for families of linear systems (Q1965274)

Consider a triple of matrices \((A,B,C)\) connected with the linear control system \[ \dot{x}=Ax+Bu,\quad y=Cx. \] The authors introduce a new equivalence relation on the space \(M\) of all triples based on the notion of a \(\rho\)-symbol. For a transverse family \(\phi:\Lambda \to M\), this equivalence relation induces a stratification over the parameter space \(\Lambda\). The authors describe singularities of the corresponding bifurcation diagrams for some few-parameter families and establish the genericity of these families.