On the canonical structure of regular pencil of singular matrix-functions

Abstract

The work is devoted to investigation of the canonical structure of regular, in domain of definition ${\cal U}\subseteq {\mathbb R}^{m}$, the pencil of matrix-functions $A(x)+\lambda B(x)$. It is supposed that $\det A(x)\equiv 0$ and $\det B(x)\equiv 0\;\; \forall \ x \in {\cal U}$, and all roots of the characteristic equation $\det(A(x)+\lambda B(x))=0$ with $\lambda=\lambda (x)\in C^{p}({\cal U})$, are of constant multiplicity.