TY - JOUR N2 - 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. L1 - http://journals.pan.pl/Content/113173/PDF/18_613-620_01006_Bpast.No.67-3_06.02.20.pdf L2 - http://journals.pan.pl/Content/113173 PY - 2019 IS - No. 3 EP - 620 DO - 10.24425/bpasts.2019.129659 KW - principle of minimum energy losses KW - optimal and suboptimal control KW - power series KW - operators of multiple differentiation or integration KW - decomposition of a rational function A1 - Siwczyński, M. A1 - Żaba, S. A1 - Drwal, A. VL - 67 DA - 30.06.2019 T1 - Energy-optimal current distribution in an electrical network – controlling by the differential or the integral systems SP - 613 UR - http://journals.pan.pl/dlibra/publication/edition/113173 T2 - Bulletin of the Polish Academy of Sciences Technical Sciences ER -