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Volumn 40, Issue 1-8, 2000, Pages 483-496

A survey of some classical and modern developments of stability theory

Author keywords

Comparison principle; Integral inequality; Large scale systems; Liapunov matrix functions; Liapunov stability; Limiting equations; Non classical stability

Indexed keywords

FUNCTIONS; LARGE SCALE SYSTEMS; LYAPUNOV METHODS; MATHEMATICAL MODELS; MATRIX ALGEBRA; NONLINEAR CONTROL SYSTEMS; ORDINARY DIFFERENTIAL EQUATIONS; THEOREM PROVING; VECTORS;

EID: 0034172588     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(00)85027-0     Document Type: Article
Times cited : (15)

References (68)
  • 2
    • 0002153562 scopus 로고
    • Limiting equations and stability of nonautonomous ordinary differential equations
    • J.P. La-Salle (Ed.), SIAM, Philadelphia
    • Z. Artstein, Limiting equations and stability of nonautonomous ordinary differential equations, in: J.P. La-Salle (Ed.), The Stability of Dynamical Systems, SIAM, Philadelphia, 1976 pp. 57-76.
    • (1976) The Stability of Dynamical Systems , pp. 57-76
    • Artstein, Z.1
  • 5
    • 0009255657 scopus 로고
    • Dynamical systems in the space of continuous functions
    • (in Russian)
    • M.V. Bebutov, Dynamical systems in the space of continuous functions, Dokl. Akad. Nauk SSSR 27 (1940) 904-906 (in Russian).
    • (1940) Dokl. Akad. Nauk SSSR , vol.27 , pp. 904-906
    • Bebutov, M.V.1
  • 9
    • 0002996269 scopus 로고
    • A generalization of a lemma of Bellman and its application to uniqueness problem of differential equations
    • I.A. Bihari, A generalization of a lemma of Bellman and its application to uniqueness problem of differential equations, Acta Math. Anal. Appl. 33 (1977) 77-81.
    • (1977) Acta Math. Anal. Appl. , vol.33 , pp. 77-81
    • Bihari, I.A.1
  • 11
    • 0001924760 scopus 로고    scopus 로고
    • Stability, stabilization, regulation using vector norms
    • A. Fossard, D. Normand-Cyrot, Chapman & Hall, London
    • P. Borne, J.P. Richard et al., Stability, stabilization, regulation using vector norms, in: A. Fossard, D. Normand-Cyrot, Non-Linear Systems: Stability and Stabilization, Vol. 2, Chapman & Hall, London, 1996, pp. 45-90.
    • (1996) Non-linear Systems: Stability and Stabilization , vol.2 , pp. 45-90
    • Borne, P.1    Richard, J.P.2
  • 12
    • 0007309937 scopus 로고
    • New method of approximate integration of differential equations
    • Nauka, Moscow, (in Russian)
    • S.A. Chaplygin, New method of approximate integration of differential equations, in: Izbran. Trudy: Mat. i Mekh., Nauka, Moscow, 1954, 490-583 (in Russian).
    • (1954) Izbran. Trudy: Mat. i Mekh. , pp. 490-583
    • Chaplygin, S.A.1
  • 13
    • 0000873060 scopus 로고
    • To the problem on estimates of approximate integrations
    • (in Russian)
    • N.G. Chetayev, To the problem on estimates of approximate integrations, Prikl. Mat. Mekh. 21 (1957) 419-421 (in Russian).
    • (1957) Prikl. Mat. Mekh. , vol.21 , pp. 419-421
    • Chetayev, N.G.1
  • 14
    • 0002277283 scopus 로고
    • Total stabiity properties by means of limiting equations
    • A. D'Anna, Total stabiity properties by means of limiting equations, Funkc. Ekvacioj. 27 (1984) 201-209.
    • (1984) Funkc. Ekvacioj. , vol.27 , pp. 201-209
    • D'Anna, A.1
  • 16
    • 0007257059 scopus 로고
    • The Gronwall type lemmas and applications
    • Universitatii din Timisoara
    • S.S. Dragomir, The Gronwall type lemmas and applications, Monografii Matematice, Universitatii din Timisoara, Vol. 29, 1987.
    • (1987) Monografii Matematice , vol.29
    • Dragomir, S.S.1
  • 18
    • 0007257060 scopus 로고
    • On multi-level absolute stability analysis of large-scale systems
    • Lj.T. Grujić, On multi-level absolute stability analysis of large-scale systems, Teoretski prilog Automatica, Part 1, 8 (1974) 67-72;
    • (1974) Teoretski Prilog Automatica, Part 1 , vol.8 , pp. 67-72
    • Grujić, Lj.T.1
  • 20
    • 0007260306 scopus 로고
    • Masinski Fakultet of Beograd University, Beograd
    • Lj.T. Grujić, Stabilnost velikih sistema, Masinski Fakultet of Beograd University, Beograd, 1974.
    • (1974) Stabilnost Velikih Sistema
    • Grujić, L.T.1
  • 23
    • 0002513583 scopus 로고
    • Phase space for retarded equations with infinite delay
    • J.K. Hale, J. Kato, Phase space for retarded equations with infinite delay, Funkc. Ekvacioj. 21 (1978) 11-41.
    • (1978) Funkc. Ekvacioj. , vol.21 , pp. 11-41
    • Hale, J.K.1    Kato, J.2
  • 24
    • 51249193789 scopus 로고
    • Zur Theorie der Systeme gevonlicher Differentialgleichungen
    • E. Kamke, Zur Theorie der Systeme gevonlicher Differentialgleichungen, Acta. Matematica 58 (1932) 57-85.
    • (1932) Acta. Matematica , vol.58 , pp. 57-85
    • Kamke, E.1
  • 25
    • 0001385795 scopus 로고
    • Some considerations to the fundamental theory of infinite delay equations
    • F. Kappel, N. Shappacher, Some considerations to the fundamental theory of infinite delay equations, Differential Equations 37 (1980) 141-183.
    • (1980) Differential Equations , vol.37 , pp. 141-183
    • Kappel, F.1    Shappacher, N.2
  • 36
    • 0006485863 scopus 로고
    • USSR Academy of Science, Moscow, (in Russian)
    • Academician A.M. Lyapunov: "Collected Papers", USSR Academy of Science, Moscow, Vol. II, 1956, pp. 5-263 (in Russian);
    • (1956) Lyapunov: "Collected Papers" , vol.2 , pp. 5-263
    • Academician, A.M.1
  • 37
    • 0001525304 scopus 로고
    • Problème général de la stabilité du mouvement
    • (French translation)
    • Problème général de la stabilité du mouvement, Ann. Fac. Toulouse 9 (1907) 203-274 (French translation);
    • (1907) Ann. Fac. Toulouse , vol.9 , pp. 203-274
  • 38
    • 0007327799 scopus 로고
    • Princeton Univerrsity Press, Princeton, (English translation)
    • also in: Annals of Mathematics Study, Vol. 17, Princeton Univerrsity Press, Princeton, 1949 (English translation);
    • (1949) Annals of Mathematics Study , vol.17
  • 39
    • 84863341615 scopus 로고
    • (English translation) also the book, Tylor & Francis, London, 1992 (English translation)
    • in: Int. J. Control 55 (1992) 531-773 (English translation); also the book, Tylor & Francis, London, 1992 (English translation).
    • (1992) Int. J. Control , vol.55 , pp. 531-773
  • 52
    • 0001892436 scopus 로고
    • On some methods of theory of technical stability
    • (in Russian)
    • N.D. Moiseyev. On some methods of theory of technical stability, Trudy VVIA im. Zhukovskogo, issue 135 (1945) 72-81 (in Russian).
    • (1945) Trudy VVIA Im. Zhukovskogo , Issue.135 , pp. 72-81
    • Moiseyev, N.D.1
  • 53
    • 0000454689 scopus 로고
    • On stability of motion with respect to linear approximation
    • (in Russian)
    • A.S. Oziraner, On stability of motion with respect to linear approximation, Prikl. Mat. Mekh. 41 (1977) 413-421 (in Russian).
    • (1977) Prikl. Mat. Mekh. , vol.41 , pp. 413-421
    • Oziraner, A.S.1
  • 58
    • 84968510092 scopus 로고
    • Nonautonomous differential equations and topological dynamics 1. the basic theory
    • G.R. Sell, Nonautonomous differential equations and topological dynamics 1. The basic theory, Trans. Amer. Math. Soc. 127 (1967) 241-262.
    • (1967) Trans. Amer. Math. Soc. , vol.127 , pp. 241-262
    • Sell, G.R.1
  • 59
    • 67649318175 scopus 로고
    • Nonautonomous differential equations and topological dynamics II. Limiting equations
    • G.R. Sell, Nonautonomous differential equations and topological dynamics II. Limiting equations, Trans. Amer. Math. Soc. 127 (1967) 263-283.
    • (1967) Trans. Amer. Math. Soc. , vol.127 , pp. 263-283
    • Sell, G.R.1
  • 61
    • 0007317324 scopus 로고
    • Author's Abstract of Kandidat Dissertation in Physicomathematical Sciences, Institute of Mechanics NASU, Kiev, (in Russian)
    • V.V. Shegai, Application of matrix Liapunov functions in stability theory, Author's Abstract of Kandidat Dissertation in Physicomathematical Sciences, Institute of Mechanics NASU, Kiev, 1986 (in Russian).
    • (1986) Application of Matrix Liapunov Functions in Stability Theory
    • Shegai, V.V.1
  • 62
    • 0007190874 scopus 로고
    • Large-scale dynamical systems
    • North-Holland, New York
    • D.D. Šiljak, Large-scale dynamical systems. Stability and Structure, North-Holland, New York, 1978.
    • (1978) Stability and Structure
    • Šiljak, D.D.1
  • 67
    • 0000560365 scopus 로고
    • Systemes des equations et des inequalites differentielles ordinaries aux deuxiemes members monotones et leur applications
    • T. Wazewski, Systemes des equations et des inequalites differentielles ordinaries aux deuxiemes members monotones et leur applications, Annales de la sosiete Polonaise de mathemematiques 23 (1950) 112-166.
    • (1950) Annales de la Sosiete Polonaise de Mathemematiques , vol.23 , pp. 112-166
    • Wazewski, T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.