The method of Ljapunov functions in the stability problem for motion with respect to a part of the variables. (English. Russian original) Zbl 0272.34070
J. Appl. Math. Mech. 36, 341-362 (1972); translation from Prikl. Mat. Mekh. 36, 364-384 (1972).
MSC:
| 34D20 | Stability of solutions to ordinary differential equations |
| 70K20 | Stability for nonlinear problems in mechanics |
References:
| [1] | Liapunov, A. M., General Problem of the Theory of Motion (1950), Gostekhizdat: Gostekhizdat Moscow-Leningrad · Zbl 0041.32204 |
| [2] | Malkin, I. G., On the Liapunov-stability of motion, Mat. Sb., Vol. 3, N≗1 (1938), (45) |
| [3] | Rumiantsev, V. V., On the stability of motion relative to a part of the variables (1957), Vestnik Moskov. Gos. Univ, N≗4 |
| [4] | Zubov, V. I., Mathematical Methods for Investigating Automatic Control Systems (1959), Sudpromgiz: Sudpromgiz Leningrad · Zbl 0088.10102 |
| [5] | Halanay, A., Differential equations, stability, oscillations, time lags (1966), Acad. Press: Acad. Press N.Y · Zbl 0144.08701 |
| [6] | Corduneanu, C., Sur la stabilite partielle. Revue Roumaine de Math, Pures et Appl, Vol. 9, N≗3 (1964) · Zbl 0134.07104 |
| [7] | Matrosov, V. M., Development of the method of Liapunov functions in the stability theory of motion, (Proc. Second All-Union Congress on Theoret. and Appl. Mech., Vol. 1 (1965), Nauka: Nauka Moscow), 112-125 |
| [8] | Rouche, N.; Peiffer, K., Le théorème de Lagrange-Dirichlet et la deuxième me’thode de Liapounoff, Ann. Soc. scient.de Bruxelles, Vol. 81, N≗1 (1967), Ser. 1 · Zbl 0146.32601 |
| [9] | Peiffer, K.; Rouche, N., Liapunov’s second method applied to partial stability, J. de mecanique, Vol. 8, N≗2 (1969) · Zbl 0206.09806 |
| [10] | Rumiantsev, V. V., (On the stability with respect to a part of the variables Symp. Math.. On the stability with respect to a part of the variables Symp. Math., Meccanica non lineare e stabilita, Vol. 6 (1971), Acad. Press: Acad. Press L.—N.Y), 243-265, 23-26 febbrario 1970 · Zbl 0226.34047 |
| [11] | Corduneanu, C., (Some problems concerning partial stability. Symp. Math. Some problems concerning partial stability. Symp. Math, Meccanica non-lineare e stabilita, Vol. 6 (1971), Acad. Press: Acad. Press L.— N.Y), 141-154, 23 - 26 febbrario 1970 · Zbl 0223.34047 |
| [12] | Oziraner, A. S., A contribution to the stability of motion relative to a part of the variables, (Mat., Mekh. (1971), Vestnik Moskov. Gos. Univ), N≗1 · Zbl 0498.70032 |
| [13] | Risito, C., Sulla stabilita asinotica parziale, Annali di Mathematica purra ed applicata, Vol. 84, 279-292 (1970), Ser. 6 · Zbl 0213.10602 |
| [14] | Rumianstev, V. V., On asymptotic stability and instability of motion with respect to a part of the variables, PMM, Vol. 35, N≗1 (1971) · Zbl 0265.34069 |
| [15] | Oziraner, A. S., On asymptotic stability with respect to a part of the variables, (Mat., Mekh. (1972), Vestnik Moskov. Cos. Univ), N≗1 · Zbl 0618.34045 |
| [16] | Antosiewicz, H. A., A survey of Lyapunov’s second method. Contributions to the theory of nonlinear oscilations (1958), Princeton University Press · Zbl 0082.30102 |
| [17] | Krasovskii, N. N., Liapunov’s second method in the stability theory of motion, (Proc. All-Union Congress on Theoret, and Appl. Mech (1962), Izdat. Akad. Nauk SSSR: Izdat. Akad. Nauk SSSR Moscow) · Zbl 0109.06001 |
| [18] | Cesari, L., Asymptotic Behavior and Stability of Solutions of Ordinary Differential Equations (1964), Mir: Mir Moscow · Zbl 0121.07203 |
| [19] | Rumianstev, V. V., Method of Liapunov functions in the stability theory of motion, (50 Years of Mechanics in the USSR, Vol. 1 (1968), Nauka: Nauka Moscow), 7-66 |
| [20] | Krasovskii, N. N., Certain Problems in the Stability Theory of Motion (1959), Fizmatgiz: Fizmatgiz Moscow · Zbl 0085.07202 |
| [21] | Chetaev, N. G., Stability of Motion (1965), Nauka: Nauka Moscow · Zbl 0061.42004 |
| [22] | Corduneanu, C., Application of differential inequalities in stability theory, ((1960), Analile Stiit. Univ., Al. i “Cisa” denias), 47-58, Sec.1, N≗6 · Zbl 0108.27802 |
| [23] | Wazewski, T., Systèmes des équations et des inégalités différentielles ordinaires aux deuxièmes membres monotones et leurs applications, Ann. Soc. Pol. Math., Vol. 23 (1950) · Zbl 0041.20705 |
| [24] | Persidskii, K. P., (On the stability of the solutions of differential equations, Vol. 97 (195), Izv. Akad, Nauk KazSSR), N≗4 · Zbl 0463.01023 |
| [25] | Demidovich, B. P., (Lectures on the Mathematical Theory of Stability (1967), Nauka: Nauka Moscow) · Zbl 0155.41601 |
| [26] | Matrosov, V. M., On the theory of stability of motion, PMM, Vol. 26, N≗6 (1962) · Zbl 0125.05003 |
| [27] | Nemytskii, V. V.; Stepanov, V. V., Qualitative Theory of Differential Equations (1949), Gostekhizdat: Gostekhizdat Moscow-Leningrad · Zbl 0089.29502 |
| [28] | LaSalle, J.; Lefschetz, S., Stability Investigation by Liapunov’s Direct Method (1964), Mir: Mir Moscow · Zbl 0116.06504 |
| [29] | Barbashin, E. A., Introduction to Stability Theory (1967), Nauka: Nauka Moscow · Zbl 0198.19703 |
| [30] | Marachkov, V. P., On one stability theorem, (Obshch, i Nauchno-Issled. Inst. Mat. i Mekh., Kazan.Univ., Vol.12 (1940), Izv. Fiz.-Mat), Ser. 3 |
| [31] | Oziraner, A. S., Problem of the invertibility of Marachkov’s theorem on asymptotic stability, Vestnik Moskov. Gos. Univ., Mat., Mekh., N≗ 3 (1971) · Zbl 0224.34049 |
| [32] | Rumiantsev, V. V., On the optimal stabilization of controlled systems, PMM, Vol. 34, N≗3 (1970) · Zbl 0215.59903 |
| [33] | Natanson, I. P., Theory of Functions of a Real Variable (1957), Gostekhizdat: Gostekhizdat Moscow · Zbl 0064.29102 |
| [34] | Sobolev, V. I., (Lectures on the Supplementary Chapters of Mathematical Analysis (1968), Nauka: Nauka Moscow) |
| [35] | Malkin, I. G., Stability Theory of Motion (1966), Nauka: Nauka Moscow · Zbl 0136.08502 |
| [36] | Barbashin, E. A.; Krasovskii, N. N., On the stability in-the-large of motion, Dokl. Akad. Nauk SSSR, Vol. 86, N≗3 (1952) |
| [37] | Barbashin, E. A.; Krasovskii, N. N., On the existence of the Liapunov function in asymptotic overall stability, PMM, Vol. 18, N≗3 (1954) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
