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Volumn 34, Issue 1, 1996, Pages 124-160

A smooth converse lyapunov theorem for robust stability

Author keywords

Lyapunov function techniques; Nonlinear stability; Robust stability; Stability with respect to sets

Indexed keywords

ASYMPTOTIC STABILITY; CONTROL SYSTEM ANALYSIS; CONTROL SYSTEM SYNTHESIS; FUNCTIONS; LYAPUNOV METHODS; ROBUSTNESS (CONTROL SYSTEMS); SYSTEM STABILITY;

EID: 0029775547     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012993259981     Document Type: Article
Times cited : (718)

References (33)
  • 1
    • 0004243911 scopus 로고
    • Birkhäuser Boston, Cambridge, MA
    • J.-P. AUBIN, Viability Theory, Birkhäuser Boston, Cambridge, MA, 1991.
    • (1991) Viability Theory
    • Aubin, J.-P.1
  • 8
    • 0000478285 scopus 로고
    • Stability analysis of the orbits of control systems
    • N. KALOUPTSIDIS AND D. L. ELLIOTT, Stability analysis of the orbits of control systems, Math. Systems Theory, 15 (1982), pp. 323-342.
    • (1982) Math. Systems Theory , vol.15 , pp. 323-342
    • Kalouptsidis, N.1    Elliott, D.L.2
  • 10
    • 0003081108 scopus 로고
    • Eventual stability in general control systems
    • P. E. KLOEDEN, Eventual stability in general control systems, J. Differential Equations, 19 (1975), pp. 106-124.
    • (1975) J. Differential Equations , vol.19 , pp. 106-124
    • Kloeden, P.E.1
  • 11
    • 0343970454 scopus 로고
    • General control systems
    • (Proceedings, Canberra, Australia, 1977), A. Bold and B. Eckmann, eds., Springer-Verlag, New York
    • _, General control systems, in Mathematical Control Theory (Proceedings, Canberra, Australia, 1977), A. Bold and B. Eckmann, eds., Springer-Verlag, New York, 1978, pp. 119-137.
    • (1978) Mathematical Control Theory , pp. 119-137
  • 13
    • 0002585302 scopus 로고
    • On the inversion of Lyapunov's second theorem on stability of motion
    • J. KURZWEIL, On the inversion of Lyapunov's second theorem on stability of motion, Amer. Math. Soc. Transl. Ser. 2, 24 (1956), pp. 19-77.
    • (1956) Amer. Math. Soc. Transl. Ser. 2 , vol.24 , pp. 19-77
    • Kurzweil, J.1
  • 16
    • 0042421421 scopus 로고
    • Ph.D. thesis, Rutgers, The State University of New Jersey, New Brunswick, NJ
    • Y. LIN, Lyapunov Function Techniques for Stabilization, Ph.D. thesis, Rutgers, The State University of New Jersey, New Brunswick, NJ, 1992.
    • (1992) Lyapunov Function Techniques for Stabilization
    • Lin, Y.1
  • 18
    • 0000682499 scopus 로고
    • Contributions to stability theory
    • J. L. MASSERA, Contributions to stability theory, Ann. of Math., 64 (1956), pp. 182-206.
    • (1956) Ann. of Math. , vol.64 , pp. 182-206
    • Massera, J.L.1
  • 19
    • 0002969701 scopus 로고
    • Design of stable control systems subject to parametric perturbation
    • A. M. MEILAKHS, Design of stable control systems subject to parametric perturbation, Avtomat. i Telemekh., 10 (1978), pp. 5-15.
    • (1978) Avtomat. i Telemekh. , vol.10 , pp. 5-15
    • Meilakhs, A.M.1
  • 20
    • 0024702510 scopus 로고
    • Criteria of asymptotic stability of differential and difference inclusions encountered in control theory
    • A. P. MOLCHANOV AND Y. S. PYANITSKIY, Criteria of asymptotic stability of differential and difference inclusions encountered in control theory, Systems Control Lett., 13 (1989), pp. 59-64.
    • (1989) Systems Control Lett. , vol.13 , pp. 59-64
    • Molchanov, A.P.1    Pyanitskiy, Y.S.2
  • 21
    • 0040444350 scopus 로고
    • Construction of a smooth Lyapunov function for an asymptotically stable set
    • T. NADZIEJA, Construction of a smooth Lyapunov function for an asymptotically stable set, Czechoslovak Math. J., 115 (1990), pp. 195-199.
    • (1990) Czechoslovak Math. J. , vol.115 , pp. 195-199
    • Nadzieja, T.1
  • 22
    • 0009443490 scopus 로고
    • Inverse of Lyapunov's second theorem for measurable functions
    • Bordeaux, France, M. Fliess, ed., IFAC Publications
    • L. ROSIER, Inverse of Lyapunov's second theorem for measurable functions, in Proceedings of Nonlinear Control Systems Design Symposium, Bordeaux, France, 1992, M. Fliess, ed., IFAC Publications, pp. 655-660.
    • (1992) Proceedings of Nonlinear Control Systems Design Symposium , pp. 655-660
    • Rosier, L.1
  • 23
    • 0001313324 scopus 로고
    • Stability in general control systems
    • E. O. ROXIN, Stability in general control systems, J. Differential Equations, 1 (1965), pp. 115-150.
    • (1965) J. Differential Equations , vol.1 , pp. 115-150
    • Roxin, E.O.1
  • 24
    • 0010049905 scopus 로고
    • Stability under perturbations in generalized dynamical systems
    • J. P. LaSalle and S. Lefschetz, eds., Academic Press, New York
    • P. SEIBERT, Stability under perturbations in generalized dynamical systems, in International Symposium on Nonlinear Differential Equations and Nonlinear Mechanics, J. P. LaSalle and S. Lefschetz, eds., Academic Press, New York, 1963, pp. 463-473.
    • (1963) International Symposium on Nonlinear Differential Equations and Nonlinear Mechanics , pp. 463-473
    • Seibert, P.1
  • 25
    • 0024647058 scopus 로고
    • Smooth stabilization implies coprime factorization
    • E. D. SONTAG, Smooth stabilization implies coprime factorization, IEEE Trans. Automat. Control, AC-34 (1989), pp. 435-443.
    • (1989) IEEE Trans. Automat. Control , vol.AC-34 , pp. 435-443
    • Sontag, E.D.1
  • 27
    • 0029288045 scopus 로고
    • On characterizations of the input-to-stale stability property
    • E. D. SONTAG AND Y. WANG, On characterizations of the input-to-stale stability property, Systems Control Lett., 24 (1995), pp. 351-359.
    • (1995) Systems Control Lett. , vol.24 , pp. 351-359
    • Sontag, E.D.1    Wang, Y.2
  • 28
    • 0024943237 scopus 로고
    • A Lyapunov description of stability in control systems
    • J. TSINIAS, A Lyapunov description of stability in control systems, Nonlinear Anal., 13 (1989), pp. 63-74.
    • (1989) Nonlinear Anal. , vol.13 , pp. 63-74
    • Tsinias, J.1
  • 29
    • 0001309053 scopus 로고
    • Prolongations and stability analysis via Lyapunov functions of dynamical polysystems
    • J. TSINIAS AND N. KALOUPTSIDIS, Prolongations and stability analysis via Lyapunov functions of dynamical polysystems, Math. Systems Theory, 20 (1987), pp. 215-233.
    • (1987) Math. Systems Theory , vol.20 , pp. 215-233
    • Tsinias, J.1    Kalouptsidis, N.2
  • 30
    • 0003039692 scopus 로고
    • Lyapunov functions and stability of dynamical polysystems
    • J. TSINIAS, N. KALOUPTSIDIS, AND A. BACCIOTTI, Lyapunov functions and stability of dynamical polysystems, Math. Systems Theory, 19 (1987), pp. 333-354.
    • (1987) Math. Systems Theory , vol.19 , pp. 333-354
    • Tsinias, J.1    Kalouptsidis, N.2    Bacciotti, A.3
  • 31
    • 84968514083 scopus 로고
    • Smoothing derivatives of functions and applications
    • F. W. WILSON, JR., Smoothing derivatives of functions and applications, Trans. Amer. Math. Soc., 139 (1969), pp. 413-428.
    • (1969) Trans. Amer. Math. Soc. , vol.139 , pp. 413-428
    • Wilson Jr., F.W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.