Determinants of the matrices of solutions to the standard and positive linear electrical circuits

Abstract

Determinants of the matrices of solutions to the standard and positive time-invariant and time-varying linear electrical circuits are addressed. Necessary and sufficient conditions for the positivity and asymptotic stability of the linear time-varying electrical circuits are established. It is shown that the determinants of the matrices of solutions to the standard and positive linear electrical circuits are nonzero and they decrease to zero for time tending to infinity if the electrical circuit contains at least one resistance and tends to 1 if the electrical circuit does not contain resistances. Determinants of the matrices of solutions of asymptotically stable electrical circuits tend to zero for time tending to infinity.