Stability problem of time varying circuit
DOI:
https://doi.org/10.3103/S0735272712020057Keywords:
time varying circuit, method of complex amplitudes, continued fraction, complex frequency, free process, necessary and sufficient condition of stabilityAbstract
Adequate mathematic apparatus of time varying circuit is the system of two linear differential equations of the first order or linear differential equation the second order. In both cases coefficients are functions dependent on argument (time). Enormous number of publications devoted to analysis of this equation stability, and as a result we have obtained many sufficient conditions of stability. Nevertheless available results do not give complete solution of the problem, moreover, there is no analysis of the fact how much well-known stability criteria are approximate to complete solution. In this paper, using radio circuit methods, it is formulated stability problem of time varying circuit in form, convenient for computer analysis.
References
V. V. Beloglazov, N. D. Biryuk, and V. V. Yurgelas, “Continued fractions in time varying circuits analysis,” Izv. Vyssh. Uchebn. Zaved., Radioelektron. 53 (6), 22 (2010) [Radioelectron. Commun. Syst. 53 (6), 299 (2010)].
Yu. T. Velichko, Theoretical Principles of Radio Engineering Circuits (LDU, Lviv, 1966) [in Ukrainian].
V. F. Zaytsev and A. D. Polyanin, Handbook of Linear Ordinary Differential Equations (Faktorial, Moscow, 1997) [in Russian].
N. V. Mak-Lakhlan, Mathew Functions Theory and Application (Izdat. Inostr. Lit., Moscow, 1953) [in Russian].
V. A. Taft, Spectral Methods of Non-Stationery Circuits and Systems Calculation (Energiya, Moscow, 1978) [in Russian].
