In the complex RLC network, apart from the currents flows arising from
the normal laws of Kirchhoff, other distributions of current, resulting
from certain optimization criteria, may also be received. This paper is
the development of research on distribution that meets the condition of
the minimum energy losses within the network called energy-optimal
distribution. Optimal distribution is not reachable itself, but in order
to trigger it off, it is necessary to introduce the control system in
current-dependent voltage sources vector, entered into a mesh set of
a complex RLC network. For energy-optimal controlling, to obtain the
control operator, the inversion of **R**(s) operator is required. It
is the matrix operator and the dispersive operator (it depends on
frequency). Inversion of such operators is inconvenient because it is
algorithmically complicated. To avoid this the operator **R**(s) is
replaced by the **R’** operator which is a matrix, but
non-dispersive one (it does not depend on s). This type of control is
called the suboptimal control. Therefore, it is important to make
appropriate selection of the **R’** operator and hence the
suboptimal control. This article shows how to implement such control
through the use of matrix operators of multiple differentiation or
integration. The key aspect is the distribution of a single rational
function *H*(*s*) in a series of ‘*s*’ or ‘*s*⁻¹’.
The paper presents a new way of developing a given, stable rational
transmittance with real coefficients in power series of ‘*s*/*s*⁻¹՚.
The formulas to determine values of series coefficients (with ‘*s*/*s*⁻¹’)
have been shown and the conditions for convergence of
differential/integral operators given as series of ‘*s*/*s*⁻¹’
have been defined.