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- Title
Construction of algebraic-differential equations with given smooth and impulsive behaviour.
- Authors
KARAMPETAKIS, NICHOLAS P.
- 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]rxr (with det A((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.
- Subjects
ALGEBRAIC equations; LINEAR systems; NUMERICAL solutions to differential equations; IMPULSIVE differential equations; POLYNOMIALS; MATHEMATICAL models
- Publication
IMA Journal of Mathematical Control & Information, 2015, Vol 32, Issue 1, p195
- ISSN
0265-0754
- Publication type
Article
- DOI
10.1093/imamci/dnt041