Wyniki wyszukiwania - BazTech

Ograniczanie wyników

1 International Journal of Applied Mathematics and Computer Science

1 2020

Znaleziono wyników: 1

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: extremal properties

Sortuj według:

Ogranicz wyniki do:

Extremal properties of linear dynamic systems controlled by Dirac’s impulse

Białas Stanisław, Górecki Henryk, Zaczyk Mieczysław

International Journal of Applied Mathematics and Computer Science

2020

Vol. 30, no. 1

75--81

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) + ∙∙∙ a₁ x’(t) + a₀ x(t) = b_m u (t) + ∙∙∙ + b₁ u’(t) + b₀ u(t) is considered with a_i, b_j >0. In the paper we assume that the polynomials M_n(s) = a_nsⁿ + ∙∙∙ + a₁s + a₀ and L_m(s) = b_ms^m + ∙∙∙ + b₁s + b₀ 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 ∊ (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, L_m, M_n), depending on the degree of the polynomial M_n(s) or L_m(s) (Theorems 5 and 6).