Electrical circuits with state-feedbacks are addressed. It is shown that by suitable choice of the gain matrices of state-feedbacks it is possible to obtain the closed-loop system matrices with nilpotency indices equal to two and their state variables are linear functions of time. The considerations are illustrated by linear electrical circuits.
One of the main problems of electrical power quality is to ensure a constant power ?ux from the supply system to the receiver, keeping in the same time the undisturbed wave form of the current and voltage signals. Distortion of signals are caused by nonlinear or time varying receivers, voltage changes or power losses in a supply system. The wave-form of the voltage of the source may also be deformed. This study seeks the optimal current and voltage wave-form by means of an optimization criteria. The optimization problem is de?ned in Hilbert space and the special functionals are minimized. The source inner impedance operator is linear and time-varying. Some examples of calculations are presented.