  We study L-systems with sectorial main operator and connections of their
impedance functions with sectorial Stieltjes and inverse Stieltjes functions.
Conditions when the main and state space operators (the main and associated
state space operators) of a given L-system have the same or not angle of
sectoriality are presented in terms of their impedance functions with
discussion provided. Detailed analysis of L-systems with one-dimensional
sectorial Shro\"odinger operator on half-line is given as well as connections
with the Kato problem on sectorial extensions of sectorial forms. Examples that
illustrate the obtained results are presented.
