The analysis of the positivity and stability of linear electrical circuits by the use of state-feedbacks is addressed. Generalized Frobenius matrices are proposed and their properties are investigated. It is shown that if the state matrix of an electrical circuit has generalized Frobenius form then the closed-loop system matrix is not positive and asymptotically stable. Different cases of modification of the positivity and stability of linear electrical circuits by state-feedbacks are discussed and necessary conditions for the existence of solutions to the problem are established.
The paper presents general solutions for fractional state-space equations. The analysis of the fractional electrical circuit in the transient state is described by the equation of the state and space equations. The results are presented for the voltage of a capacitor and current in a coil, for different alpha values. The Caputo and conformable fractional derivative definitions have been considered. At the end, the results have been obtained.
The concept of strong stability is extended for positive and compartmental linear systems. It is shown that: 1) the asymptotically stable positive and compartmental systems are strongly stable if the eigenvalues of the system matrix are distinct, 2) electrical circuits consisting of resistances, capacitances (inductances) and source voltages are strongly stable.
An analysis of a given electrical circuit using a fractional derivative. The statespace equation was developed. The dynamics of tensions described by Kirchhoff’s laws equations. The paper used the definition of the integral derivative Caputo and CDF conformable fractional definition. An electrical circuit solution using Caputo and CDF defini- tions for rectangular with zero initial conditions was developed. The results obtained using the Caputo and CDF definitions were compared. The solutions are shown for capacitor voltages, for fractional derivative orders of 0.6, 0.8, 1. The results were compared using graphs.
In the present paper results of the studies devoted to computer simulations of dielectric response of electroceramics in a frequency domain as well as analysis of the experimental data are given. As an object of investigations BiNbO4-based microwave ceramics was taken. Simulations of the hypothetical impedance response of the ceramic system were performed under assumption of the brick-layer model. A strategy for analysis and modelling of the impedance data for microwave electroceramics was discussed. On the base of the discussed strategy modelling of the dielectric response of BiNbO4 ceramics was performed with the electric equivalent circuit method. The Voigt’s and Maxwell’s circuits were taken as electric models. Parameters of the electric components of the circuits were determined and related to parameters of the ceramic object under study. It was found that fitting quality was good and changed within the range χ2 = 6.78 × 10–4 – 6.77 × 10–5 depending on the model.