Stability of phase systems. (English. Russian original) Zbl 0303.93048
Sib. Math. J. 15, 34-42 (1974); translation from Sib. Mat. Zh. 15, 49-60 (1974).
MSC:
| 93D15 | Stabilization of systems by feedback |
| 93B05 | Controllability |
| 93C15 | Control/observation systems governed by ordinary differential equations |
References:
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| [2] | Yu. N. Bakaev, Some Questions in the Nonlinear Theory of Phase Systems [in Russian], Trudy VVIA im. Zhukovskogo, Moscow (1959), p. 800. |
| [3] | E. Noldus, ?On the stability of systems having several equilibrium states,? Applied Scientific-Research,21, Nos. 3 and 4, 219-233 (1969). · Zbl 0188.46802 |
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| [5] | A. Kh. Gelig, ?Research on the stability of nonlinear discontinuous automatic control systems with several equilibrium states,? Avtomat. i Telemekh., No. 2, 153-159 (1964). |
| [6] | G. A. Leonov, ?Stability of nonlinear control systems with several equilibrium positions,? Avtomat. i Telemekh., No. 10, 23-28 (1971). |
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| [9] | G. Seifert, ?On the existence of certain solutions of nonlinear equations,? Z. Angew. Math. und Phys.,3, No. 6, 468-471 (1952). · Zbl 0053.24502 · doi:10.1007/BF02025575 |
| [10] | V. A. Tabueva, ?An estimate for the critical value of the parameter ? for the differential equation \(\ddot x + \alpha \dot x + f(z) = 0\) ,? Izv. Vyssh. Uchebn. Zavedenii. Matematika, No. 2, 227-237 (1958). · Zbl 0122.09603 |
| [11] | W. D. Hayes, ?On the equation for a damped pendulum under constant torque,? Z. Angew. Math. und Phys.,4, No. 5, 398-401 (1953). · Zbl 0053.24503 · doi:10.1007/BF02074983 |
| [12] | C. Bohm, ?New criteria for the existence of periodic solutions for a well-known nonlinear differential equation,? Ann. Mat. Pura ed Appl.,35, 344-353 (1953). · Zbl 0053.24504 · doi:10.1007/BF02415277 |
| [13] | M. V. Kapranov, ?Holding band for automatic phase frequency fine tuning,? Radiotekhnika, No. 12, 37-52 (1956). |
| [14] | B. I. Shakhtarin, ?A system of automatic phase frequency fine tuning with a second order filter,? Radiotekhnika i Élektronika, No. 9, 1701-1704 (1968). |
| [15] | V. M. Popov, Hyperstability of Automatic Systems [in Russian], Nauka, Moscow (1970). |
| [16] | Yu. N. Bakaev, ?The construction of operational bands and systems of automatic phase control,? Izv. Akad. Nauk SSSR, Énergetika i Avtomatika, No. 2, 132-136 (1960). |
| [17] | Yu. N. Bakaev, ?Synchronization properties of phase systems for third order automatic frequency fine tuning,? Radiotekhnika i Élektronika, No. 6, 1083-1087 (1965). |
| [18] | F. R. Gantmakher and V. A. Yakubovich, ?Absolute stability of nonlinear control systems,? Proceedings of the Second All-Union Congress on Theoretical and Applied Mechanics [in Russian], Vol. 1, Nauka, Moscow (1965), pp. 30-63. |
| [19] | V. A. Yakubovich, ?Absolute stability of nonlinear control systems in the critical cases. III,? Avtomat. i Telemekh., No. 5, 601-612 (1964). |
| [20] | R. E. Kalman, ?Physical and mathematical mechanisms of instability in nonlinear automatic control systems,? Trans. ASME, No. 3, 553-566 (1957). |
| [21] | A. Kh. Gelig and G. A. Leonov, ?Monostability of multiply connected systems with discrete monotone nonlinearities and several equilibrium positions,? Avtomat. i Telemekh., No. 6, 3-7 (1973). |
| [22] | V. A. Yakubovich, ?S-procedures in nonlinear control theory,? Vestnik Leningrad. Univer., No. 1, 62-77 (1971). · Zbl 0232.93010 |
| [23] | V. A. Yakubovich, ?Solutions of several matrix inequalities encountered in nonlinear control theory,? Dokl. Akad. Nauk SSSR,143, No. 6, 1304-1307 (1962). |
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