Szczegóły publikacji
Opis bibliograficzny
Extremal properties of linear dynamic systems controlled by Dirac's impulse / Stanisław Białas, Henryk GÓRECKI, Mieczysław ZACZYK // International Journal of Applied Mathematics and Computer Science ; ISSN 1641-876X. — 2020 — vol. 30 no. 1, s. 75–81. — Bibliogr. s. 81
Autorzy (3)
- Białas Stanisław
- AGHGórecki Henryk
- AGHZaczyk Mieczysław
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 128519 |
|---|---|
| Data dodania do BaDAP | 2020-05-06 |
| Tekst źródłowy | URL |
| DOI | 10.34768/amcs-2020-0006 |
| Rok publikacji | 2020 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Creative Commons | |
| Czasopismo/seria | International Journal of Applied Mathematics and Computer Science |
Abstract
The paper concerns the properties of linear dynamical systems described by linear differential equations, excited by the Dirac delta function. A differential equation of the form a(n)x((n)) (t) +...+a(1)x' (t) + a(0)x(t) = b(m)u((m)) (t) +...+b(1)u' (t) + b(0)u(t) is considered with a(i), b(j) > 0. In the paper we assume that the polynomials M-n(s) = a(n)s(n) +...+ a(1)s a(0) and L-m (s) = b(m)s(m) +...+ b(1)s + b(0) partly interlace. The solution of the above equation is denoted by x(t, L-m, M-n). It is proved that the function x(t, L-m , M-n) is nonnegative for t is an element of (0, infinity), and does not have more than one local extremum in the interval (0, infinity) (Theorems 1, 3 and 4). Besides, certain relationships are proved which occur between local extrema of the function x(t, L-m, M-n ), depending on the degree of the polynomial M-n(s) or L-m (s) (Theorems 5 and 6).