Abstract

This paper consists of two parts. In the first part, we present the smooth and impulsive solution space B of the system of algebraic and differential equations A(ρ) β(t)=0, ρ≔d/dt, where A(ρ)∈ℝ[ρ]r × r (with detA (ρ) ≠ 0) is given. The solution space is given in terms of finite and infinite Jordan pairs of the polynomial matrix A(ρ), and therefore a necessary introduction is given for finite and infinite zero structures of the polynomial matrix A(ρ). In the second part, we study the inverse problem: Given a smooth and impulsive solution space B, we try to find out a system of algebraic and differential equations A(ρ) β(t) = 0, ρ ≔ dt with the given solution space.

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