References
R. Z. Abdullin et al., Method of Liapunov Vector Functions in the Theory of Stability, Nauka, Moscow (1987).
L. T. Gruiich, A. A. Martynyuk, and M. Ribbens-Pavella, Stability of Large-Scale Systems under Structural and Singular Perturbations, Nauk. Dumka, Kiev (1984).
V. F. Zadorozhnyi and A. A. Martynyuk, "Solution of the general problem of aggregation as a problem of moments," Mat. Fiz., No. 14, 49–55 (1973).
A. S. Zemlyakov, "Methods of constructing a quadratic Liapunov vector function for nonlinear multiply connected systems," Tr. Kazan. Aviats. Inst.,180, 14–22 (1975).
V. I. Zubov, The Methods of A. M. Liapunov and Their Application [in Russian], Izd. LGU, Leningrad (1975).
Yu. N. Krapivnyk, "Methods of constructing Liapunov matrix functions and evaluating the region of asymptotic stability of large-scale systems," Author's Abstract of Physico-Mathematical Sciences Candidate Dissertation, Kiev (1988).
Yu. N. Krapivnyi and A. A. Martynyuk, "Method of using Liapunov matrix functions in the theory of stability," Fifth All-Union Chetaev. Conference "Analytical Mechanics, Stability, and the Control of Motion," Summary of Documents, Kazan (1987), p. 87.
Yu. N. Krapivnyi and A. A. Martynyuk, "Method of decomposition of large-scale systems in the study of the stability of motion," Prikl. Mekh.,24, No. 8 (1988).
V. Lakshmikantam, S. Liila, and A. A. Martynyuk, Stability of Motion: Congruence Method [in Russian], Nauk. Dumka, Kiev (1991).
A. P. Liapunov, General Problem of Stability of Motion [in Russian], ONTI, Moscow (1935),
A. A. Martynyuk, Stability of Motion of Complex Systems [in Russian], Nauk. Dumka, Kiev (1975).
A. A. Martynyuk and K. Begmuratov, "Hierarchical Liapunov matrix function and its application," Electron. Modelir.,13, No. 5, 3–9 (1991).
A. A. Martynyuk and Yu. N. Krapivnyi, "Nonlinear congruent systems and the stability of large-scale systems," Prikl. Mekh.,23, No. 4, 75–80 (1987).
A. A. Martynyuk and V. V. Shegai, "Toward a theory of the stability of autonomous systems," Prikl. Mekh.,22, No. 4, 97–102 (1986).
A. A. Martynyuk and V. V. Shegai, "Study of the stability of large-scale systems on the basis of Liapunov matrix functions," Prikl. Mekh.,22, No. 6, 106–113 (1986).
V. M. Matrosov, "Toward a theory of the stability of motion," Prikl. Mat. Mekh., No. 6, 992–1000 (1962).
V. M. Matrosov, "Method of Liapunov vector functions in feedback systems," Avtom. Telemekh., No. 9, 63–75 (1979).
V. V. Shegai, "Use of Liapunov matrix functions in the theory of the stability of motion," Author's Abstract of Physico-Mathematical Sciences Candidate Dissertation, In-t Mekhaniki AN Ukr. SSR, Kiev (1986).
M. Aoki, "Control of large-scale dynamic systems by aggregation," IEEE Trans. Autom. Control.,13, No. 3, 246–253 (1968).
M. Z. Djordjevic, "Stability analysis of interconnected systems whose subsystems may be unstable," Large Scale Systems, No. 5, 255–262 (1983).
F. N. Bailey, "The application of Liapunov's second method to interconnected systems," SIAM J. Control, No. 3, 443–462 (1966).
R. Bellman, "Vector Liapunov functions," SIAM J. Control, No. 1, 32–34 (1962).
Lj. T. Grujic, A. A. Martynyuk, and M. Ribbens-Pavella, Large Scale Systems Stability under Structural and Singular Perturbations, Springer Verlag, Berlin (1987).
W. Hahn, Stability of Motion, Springer Verlag, Berlin (1967).
J. K. Hale, "Dynamical systems and stability," J. Math. Anal. Appl.,26, 39–59 (1969).
J. P. Lasalle, "Vector Liapunov functions," Bull. Inst. Math., Acad. Sinica, No. 3, 139–150 (1975).
A. A. Martynyuk, "The Liapunov matrix function," Nonlinear Analysis,8, No. 10, 1223–1226 (1984).
A. N. Michel and R. K. Miller, Qualitative Analysis of Large Scale Dynamical Systems, Academic Press, New York (1977).
D. D. Siljak, Large Scale Dynamic Systems: Stability and Structure, North-Holland, New York (1987).
M. Vidyasagar, Output Analysis of Large-Scale Interconnected Systems: Decomposition, Well-Posedness, and Stability, Springer Verlag (1981).
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S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of the Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 31, No. 9, pp. 3–14, September, 1995.
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Martynyuk, A.A. Forms of aggregation in the study of the stability of motion of large-scale systems. Criteria of stability (review). Int Appl Mech 31, 683–694 (1995). https://doi.org/10.1007/BF00846853
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DOI: https://doi.org/10.1007/BF00846853