- Tytuł:
- Extremal properties of linear dynamic systems controlled by Dirac’s impulse
- Autorzy:
-
Białas, Stanisław
Górecki, Henryk
Zaczyk, Mieczysław - Powiązania:
- https://bibliotekanauki.pl/articles/331114.pdf
- Data publikacji:
- 2020
- Wydawca:
- Uniwersytet Zielonogórski. Oficyna Wydawnicza
- Tematy:
-
extremal properties
Dirac's impulse
linear system
transfer function
właściwości ekstremalne
impuls Diraca
układ liniowy
funkcja przenoszenia - Opis:
- 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 an x(n) (t) + ∙∙∙ a1 x’(t) + a0 x(t) = bm u (t) + ∙∙∙ + b1 u’(t) + b0 u(t) is considered with ai, bj >0. In the paper we assume that the polynomials Mn(s) = ansn + ∙∙∙ + a1s + a0 and Lm(s) = bmsm + ∙∙∙ + b1s + b0 partly interlace. The solution of the above equation is denoted by x(t, Lm, Mn). It is proved that the function x(t, Lm, Mn) is nonnegative for t ∊ (0, ∞) , and does not have more than one local extremum in the interval (0, ∞) (Theorems 1, 3 and 4). Besides, certain relationships are proved which occur between local extrema of the function x(t, Lm, Mn), depending on the degree of the polynomial Mn(s) or Lm(s) (Theorems 5 and 6).
- Źródło:
-
International Journal of Applied Mathematics and Computer Science; 2020, 30, 1; 75-81
1641-876X
2083-8492 - Pojawia się w:
- International Journal of Applied Mathematics and Computer Science
- Dostawca treści:
- Biblioteka Nauki