Positive time-varying continuous-time linear systems and electrical circuits

Abstract

Abstract. The positivity of time-varying continuous-time linear systems and electrical circuits are addressed. Necessary and sufficient conditions for the positivity of the systems and electrical circuits are established. It is shown that there exists a large class of positive electrical circuits with time-varying parameters. Examples of positive electrical circuits are presented.

Archives of Electrical Engineering

“…where v p (t) is the control voltage (parametric function), α is the gain factor of the multiplier. The comparison of Equations ( 6), (7) shows that:…”

“…There are known works focused on the theoretical analysis in the time and in the frequency domain [1,4,[7][8][9]. The continuous time-varying system can be treated as an auxiliary tool for analysis of fractional systems [10].…”

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

“…1 with given resistance R , inductance L , capacitance C and source voltage e . The electrical circuit is described by the equation Using Kirchhoff's laws we may write for the electrical circuit the equations (16) . ,…”

“…The Lyapunov, Bohl and Perron exponents and stability of time-varying discrete-time linear systems have been investigated in [1][2][3][4][5][6]. The positivity and stability of timevarying linear systems have been addressed in [12,16,18,20,22,23,28] and the stability of continuous-time linear systems with delays in [26]. The fractional positive linear systems have been analyzed in [10,11,13,19,21,24,25,29].…”