O. G. Antonovskaya, V. I. Goryunov, Yu. P. Palochkin, Research Institute of Applied Mathematics & Cybernetics, Nizhni Novgorod, Russia

SYNCHROINFO JOURNAL. Volume 5, Number 6 (2019). P. 10-12.


The procedure of combined control synthesis under reference generator frequency, counter indexes, defining working basic and output frequency of frequency synthesizer and filter structure, using the main thesis of control theory for nonlinear systems with discrete time and the analysis of nonlinear phenomena, is discussed. The possibility of using of geometrical imaginations, based on corresponding point mapping dependence on parameters study, is noted.

Keywords: nonlinear phenomena, frequency synthesizer, transient process, mathematical model, qualitative analysis, quasi-optimal control.


[1] V. V. Shahgildyan, A. V. Pestriakov. Perspective directions of development of discrete phase synchronization systems theory for frequency synthesis and stabilization apparatus. Elektrosvyaz. No. 11, pp. 38-42.
[2] V .A. Levin, V. V. Malinovsky, S. K. Romanov. Frequency synthesizers with pulse-phase frequency auto-correction. Moscow. 1989.
[3] V. I. Goryunov, V. N. Eruslanov, M. N. Zaytseva. On synthesizer fast-action analysis under switching over a band. Technika sredstv svyazy. Ser. Technika radiosvyazy. No.3. 1986, pp.44-49.
[4] O. G. Antonovskaya, V. I. Goryunov, M. N. Zaytseva. Analysis of dynamical characteristics of basic synthesizer model. Povyshenie kachestva i effectivnosty ustroystv synchronizatsiy v systemah svyazy, Nauch.-tech. conf. Abstracts. Yaroslavl. 1993, p.25.
[5] O. G. Antonovskaya, V. I. Goryunov. On the question of frequency synthesizer self-action under all kinds of switching in interval. NNGU, NII PMK, N.Novgorod. 1999, 46  p. Dep. in VINITI 31.03.99 N 987-B99.
[6] V. V. Malinovsky. On frequency synthesizer fast-action increase by DPKD index control. Technika sredstv svyazy. Ser. Technika radiosvyazy. No. 7. 1981, pp. 96-109.
[7] V. I. Goryunov. On the theory of pulse-phase frequency autocorrection. Izv. VUZ, Priborostroenie. No.10. 1974, pp. 40-43.
[8] Reference book on automatic control theory, edited by A.A.Krasovsky. Moscow: Nauka. 1987.
[9] V. V. Shahgildyan, A. A. Lyahovkin. Frequency phase auto-correction. Moscow: Svyaz, 1996.
[10] A. V. Feldbaum, A. G. Butkovsky. Automatic control theory methods. Moscow: Nauka, 1971.
[11] V. I. Goryunov. On the feedback parameter optimization for the robust stable frequency synthesizer. Matematicheskoe modelirovanie i optimalnoe upravlenie, Vestnik NNGU. N.Novgorod. No.2(24). 2001, pp.274-281.
[12] V. I. Goryunov, V. N. Eruslanov, N. I. Lobashov. Technical capture band of one-counter frequency synthesizer. Technika sredstv svyazy. Ser. Technika radiosvyazy. No. 2. 1990, pp. 88-94.
[13] O. G. Antonovskaya, V. I. Goryunov. On construction and application of conditionally extremal Lyapunov function. Matematicheskoe modelirovanie, upravlenie i optimizatsiya, Sbornik, Gorky. 1990. Dep. VINITI 28.09.90 N 5198-B90, pp. 4-15.
[14] O. G. Antonovskaya, V. I. Goryunov. On the problem of conditionally extremal Lyapunov function construction. NNGU, NII PMK. N.Novgorod. 1993. 29 p. Dep. VINITI 27.05.93 N 1430-B93.
[15] O. G. Antonovskaya, V. I. Goryunov. Direct Luapunov method and problem of analysis by computer of interval-indefinite systems. Ustoichivost i kolebaniya nelineinyh system upravleniya. V International seminar. Moscow. 1998, p. 56.
[16] O. G. Antonovskaya, V. I. Goryunov. Quadratic Lyapunov function under its first derivative limitation condition. Matematicheskoe modelirovanie i optimalnoe upravlenie. Vestnik NNGU. N.Novgorod. No. 1(23). 2001, pp. 56-64.