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A method is proposed for calculation of transition matrices of positive electrical circuits. It is shown that if the transition matrix is presented as finite series of the Metzler matrix with real distinct eigenvalues then the coefficients of the series are nonnegative function of time. The method is applied to positive linear electrical circuits.
Minimum energy control problem for the fractional positive electrical circuits with bounded inputs is formulated and solved. Sufficient conditions for the existence of solution to the problem are established. A procedure for solving of the problem is proposed and illustrated by example of fractional positive electrical circuit.
Necessary and sufficient conditions for the positivity and reachability of electrical circuits composed of resistors, coils and capacitors are given. The minimum energy control problem for the positive electrical circuits is formulated and solved. Procedure for computation of the optimal input and minimal value of the performance index is proposed and illustrated by a numerical examples.
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