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Volumn , Issue 7, 1993, Pages 1-8

Recent advances in the stabilization problem for low dimensional systems

Author keywords

[No Author keywords available]

Indexed keywords

CONTROL THEORY; DESCRIBING FUNCTIONS; MATHEMATICAL MODELS; POLYNOMIALS; STABILIZATION; SYSTEM STABILITY; SYSTEMS ANALYSIS; THEOREM PROVING; THREE DIMENSIONAL;

EID: 0027188445     PISSN: 09629505     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1016/b978-0-08-041901-5.50006-3     Document Type: Conference Paper
Times cited : (45)

References (74)
  • 1
    • 0004029931 scopus 로고
    • Dynamical Systems I
    • Dynamical Systems I D.V. Anosov V.I. Arnold Encyclopedia of Mathematical Sciences Vol.1 1988 Springer Verlag Berlin
    • (1988)
  • 2
    • 0022661079 scopus 로고
    • “Local feedback stabilization and bifurcation control,I, Hopf bifurcation”
    • E.H. Abed J.H. Fu “Local feedback stabilization and bifurcation control,I, Hopf bifurcation” Systems and Control Letters 7 1986 11 17
    • (1986) Systems and Control Letters , vol.7 , pp. 11-17
    • Abed, E.H.1    Fu, J.H.2
  • 3
    • 0023346390 scopus 로고
    • “Local feedback stabilization and bifurcation control,II. Stationary bifurcation,”
    • E.H. Abed J.H. Fu “Local feedback stabilization and bifurcation control,II. Stationary bifurcation,” Systems and Control Letters 8 1987 467 473
    • (1987) Systems and Control Letters , vol.8 , pp. 467-473
    • Abed, E.H.1    Fu, J.H.2
  • 4
    • 85113045525 scopus 로고    scopus 로고
    • J. H. Fu and E.H. Abed, “Linear feedback stabilization of nonlinear systems,” (preprint) (to appear in Automatica ).
  • 5
    • 85113079301 scopus 로고    scopus 로고
    • J. H. Fu and E. H. Abed, “Families of Lyapunov functions for nonlinear systems in critical cases,” (preprint) (to appear in IEEE Trans. Automat. Contr. ).
  • 6
    • 0020848962 scopus 로고
    • “Stabilization with relaxed controls,”
    • Z. Artstein “Stabilization with relaxed controls,” Nonl. Anal, TMA 7 1983 1163 1173
    • (1983) Nonl. Anal, TMA , vol.7 , pp. 1163-1173
    • Artstein, Z.1
  • 7
    • 0023846469 scopus 로고
    • “Comments on the stabilizability of the angular velocity of a rigid body,”
    • D. Ayels M. Szafranski “Comments on the stabilizability of the angular velocity of a rigid body,” Systems and Control Letters 10 1988 35 39
    • (1988) Systems and Control Letters , vol.10 , pp. 35-39
    • Ayels, D.1    Szafranski, M.2
  • 8
    • 0012438663 scopus 로고
    • “Stabilization of a class of nonlinear systems by a smooth feedback,”
    • D. Ayels “Stabilization of a class of nonlinear systems by a smooth feedback,” Systems and Control Letters 5 1985 181 191
    • (1985) Systems and Control Letters , vol.5 , pp. 181-191
    • Ayels, D.1
  • 9
    • 85113062999 scopus 로고
    • A. Bacciotti Local Stabilizability of Nonlinear Control Systems 8 1992 World Scientific Press Singapore Series on Advances in Mathematics for Applied Sciences
    • (1992)
    • Bacciotti, A.1
  • 10
    • 0024305126 scopus 로고
    • “Feedback stabilization of planar nonlinear systems,”
    • W.M. Boothby R. Marino “Feedback stabilization of planar nonlinear systems,” Systems and Control Letters 12 1989 87 92
    • (1989) Systems and Control Letters , vol.12 , pp. 87-92
    • Boothby, W.M.1    Marino, R.2
  • 11
    • 85113046907 scopus 로고    scopus 로고
    • W. M. Boothby and R. Marino, “ Feedback stabilization of planar nonlinear systems II,” 28th IEEE Conf. on Decision and Control , (1989), 1970–1974.
  • 12
    • 84919219920 scopus 로고
    • “The center manifold theorem in feedback stabilization of planar, single input, systems,”
    • W.M. Boothby R. Marino “The center manifold theorem in feedback stabilization of planar, single input, systems,” Control - Theory and Advanced Technology 6 1990 517 532
    • (1990) Control - Theory and Advanced Technology , vol.6 , pp. 517-532
    • Boothby, W.M.1    Marino, R.2
  • 13
    • 0026005382 scopus 로고
    • “On the attitude stabilization of rigid spacecraft,”
    • C.I. Byrnes A. Isidori “On the attitude stabilization of rigid spacecraft,” Automatica 27 1991 87 95
    • (1991) Automatica , vol.27 , pp. 87-95
    • Byrnes, C.I.1    Isidori, A.2
  • 14
    • 0026238258 scopus 로고
    • “Asymptotic stabilization of minimum phase systems,”
    • C.I. Byrnes A. Isidori “Asymptotic stabilization of minimum phase systems,” IEEE Transac. Automat. Contr AC-36 1991 1122 1137
    • (1991) IEEE Transac. Automat. Contr , vol.AC-36 , pp. 1122-1137
    • Byrnes, C.I.1    Isidori, A.2
  • 15
    • 0026238258 scopus 로고
    • “Passivity, feedback equivalence and the global stabilization of minimum phase nonlinear systems”
    • C.I. Byrnes A. Isidori J.C. Willems “Passivity, feedback equivalence and the global stabilization of minimum phase nonlinear systems” IEEE Transac. Automat. Contr. AC-36 1991 1228 1240
    • (1991) IEEE Transac. Automat. Contr. , vol.AC-36 , pp. 1228-1240
    • Byrnes, C.I.1    Isidori, A.2    Willems, J.C.3
  • 16
    • 0003412532 scopus 로고
    • “Asymptotic stability and feedback stabilization”
    • R. Brockett “Asymptotic stability and feedback stabilization” Differential Geometric Control Theory 1983 Birkhauser Boston
    • (1983)
    • Brockett, R.1
  • 17
    • 85113058617 scopus 로고
    • J. Carr Applications of Center Manifold Theory 1981 Springer Verlag NY
    • (1981)
    • Carr, J.1
  • 18
    • 85113036091 scopus 로고
    • “Asymptotic stability in 3-space,”
    • C. Coleman “Asymptotic stability in 3-space,” L. Cesari J.P. LaSalle S. Lefschetz Contributions to the Theory of Nonlinear Oscillations - Vol. V 45 1960 Princeton Univ. Press Annals of Mathematics Studies
    • (1960)
    • Coleman, C.1
  • 19
    • 0025402690 scopus 로고
    • “A necessary condition for feedback stabilization,”
    • J.-M. Coron “A necessary condition for feedback stabilization,” Syst. Contr. Lett. 14 1990 227 232
    • (1990) Syst. Contr. Lett. , vol.14 , pp. 227-232
    • Coron, J.-M.1
  • 20
    • 0026204666 scopus 로고
    • “Adding an integrator for stabilization problem,”
    • J.-M. Coron L. Praly “Adding an integrator for stabilization problem,” Syst. Contr. Lett. 17 1991 89 105
    • (1991) Syst. Contr. Lett. , vol.17 , pp. 89-105
    • Coron, J.-M.1    Praly, L.2
  • 21
    • 85113035097 scopus 로고
    • “Stabilization of nonlinear control systems: the role of Newton diagrams,”
    • P.E. Crouch I.S. Igheneiwa “Stabilization of nonlinear control systems: the role of Newton diagrams,” International Journal of Control 49 1989 205 211
    • (1989) International Journal of Control , vol.49 , pp. 205-211
    • Crouch, P.E.1    Igheneiwa, I.S.2
  • 22
    • 85113049332 scopus 로고
    • D. Deimling Nonlinear Functional Analysis 1988 Springer Verlag New York
    • (1988)
    • Deimling, D.1
  • 23
    • 85113050031 scopus 로고
    • “Asymptotic stabilization of low dimensional systems,”
    • W.P. Dayawansa “Asymptotic stabilization of low dimensional systems,” Nonlinear Synthesis, Progress in Systems and Control Theory 9 1991 Birkhauser Boston
    • (1991)
    • Dayawansa, W.P.1
  • 24
    • 85113054208 scopus 로고    scopus 로고
    • W. P. Dayawansa and C. F. Martin, “Some sufficient conditions for the asymptotic stabilizability of three dimensional homogeneous systems,” Proc. IEEE Conf. on Decision and Control , Tampa, Dec. 1989, 1366–1370.
  • 25
    • 0024641682 scopus 로고
    • “Asymptotic Stabilization of Two Dimensional Real Analytic Systems,”
    • W.P. Dayawansa C.F. Martin “Asymptotic Stabilization of Two Dimensional Real Analytic Systems,” Systems and Control Letters 12 1989 205 211
    • (1989) Systems and Control Letters , vol.12 , pp. 205-211
    • Dayawansa, W.P.1    Martin, C.F.2
  • 26
    • 33747011548 scopus 로고
    • “A Remark on a Theorem of Andreini, Bacciotti and Stefani,”
    • W.P. Dayawansa C.F. Martin “A Remark on a Theorem of Andreini, Bacciotti and Stefani,” Syst. and Contr. Lett. 13 1989 363 364
    • (1989) Syst. and Contr. Lett. , vol.13 , pp. 363-364
    • Dayawansa, W.P.1    Martin, C.F.2
  • 27
    • 0025519724 scopus 로고
    • “Asymptotic stabilization of a class of smooth two dimensional systems,”
    • W.P. Dayawansa C. Martin G. Knowles “Asymptotic stabilization of a class of smooth two dimensional systems,” SIAM J. on Control and Optimization 28 1990 1321 1349
    • (1990) SIAM J. on Control and Optimization , vol.28 , pp. 1321-1349
    • Dayawansa, W.P.1    Martin, C.2    Knowles, G.3
  • 28
    • 85113079381 scopus 로고    scopus 로고
    • W. P. Dayawansa, C. F. Martin ans S. Samelson, “Asymptotic stabilization of three dimensional homogeneous quadratic systems,” submitted to Proc. of the 31st IEEE Conf. on Dec. and Contr
  • 29
    • 85113040935 scopus 로고    scopus 로고
    • W. P. Daywansa, C. F. Martin and S. Samelson, “Asymptotic stabilization of single input, three dimensional, homogeneous polynomial systems,” under preperation.
  • 30
    • 85113063005 scopus 로고    scopus 로고
    • W. P. Daywansa, C. F. Martin and S. Samelson, “Asymptotic stabilization of generic single input, three dimensional, homogeneous polynomial systems of a given degree,” submitted to Systems and Control Letters
  • 31
    • 33646991587 scopus 로고
    • “Uber das Verhalten der Integralkurven einer Gewohnlichen Differnetialalgleichung erster Ordnung in der Umgebung eines singularen Punktes,”
    • H. Forster “Uber das Verhalten der Integralkurven einer Gewohnlichen Differnetialalgleichung erster Ordnung in der Umgebung eines singularen Punktes,” Mathematishe Zetschrift 43 1937 271 320
    • (1937) Mathematishe Zetschrift , vol.43 , pp. 271-320
    • Forster, H.1
  • 33
    • 85113055604 scopus 로고
    • M. Golubitsky D.G. Shaeffer Singularities and Groups in Bifurication Theory 1 1985 Springer Verlag NY
    • (1985)
    • Golubitsky, M.1    Shaeffer, D.G.2
  • 34
    • 85113052299 scopus 로고
    • W. Hahn Stability of motion 1967 Springer Verlag NY
    • (1967)
    • Hahn, W.1
  • 35
    • 85113070750 scopus 로고
    • W. Hahn Stability of Motion 1967 Springer Verlag New York
    • (1967)
    • Hahn, W.1
  • 37
    • 85113068537 scopus 로고    scopus 로고
    • H. Hermes, “Homogeneous coordinates and continuous asymptotically stabilizing feedback controls,” Proceedings of the Conference on Differential Equations Applications to Stability and Control , Colorado Springs, 1989.
  • 38
    • 0022755805 scopus 로고
    • “Nilpotent approximation of control systems and distributions,”
    • H. Hermes “Nilpotent approximation of control systems and distributions,” SIAM J. Contr. Optimiz. 24 1986 731 736
    • (1986) SIAM J. Contr. Optimiz. , vol.24 , pp. 731-736
    • Hermes, H.1
  • 39
    • 0026080309 scopus 로고
    • “Asymptotic stabilizing feedback controls and the nonlinear regulator problem,”
    • H. Hermes “Asymptotic stabilizing feedback controls and the nonlinear regulator problem,” SIAM J. Contr. Optimiz. 29 1991 185 196
    • (1991) SIAM J. Contr. Optimiz. , vol.29 , pp. 185-196
    • Hermes, H.1
  • 40
    • 0026374076 scopus 로고
    • “Asymptotic stabilization of planar nonlinear systems,”
    • H. Hermes “Asymptotic stabilization of planar nonlinear systems,” Syst. Contr. Lett. 17 1991 437 445
    • (1991) Syst. Contr. Lett. , vol.17 , pp. 437-445
    • Hermes, H.1
  • 41
    • 85113045503 scopus 로고
    • A. Isidori Nonlinear Control Systems 2nd ed. 1989 Springer Verlag New York
    • (1989)
    • Isidori, A.1
  • 42
    • 0019020679 scopus 로고
    • “Dissipative dynamical systems: Basic input-output properties”
    • D.J. Hill P.J. Moylan “Dissipative dynamical systems: Basic input-output properties” J. Franklin Inst. 309 1980 327 357
    • (1980) J. Franklin Inst. , vol.309 , pp. 327-357
    • Hill, D.J.1    Moylan, P.J.2
  • 43
    • 0002757535 scopus 로고
    • “Nonlinear Oscillations,”
    • L.N. Howard “Nonlinear Oscillations,” F.C. Hopensteadt Nonlinear Oscillations in Biology 1979 Amer. Math. Soc. Providence 1 68
    • (1979) , pp. 1-68
    • Howard, L.N.1
  • 44
    • 0002597265 scopus 로고
    • “Feedback equivalence of planar systems and stabilizability,”
    • B. Jakubcyk W. Respondek “Feedback equivalence of planar systems and stabilizability,” M.A. Kaashoek J.H. van Schuppen C.A.M. Ran Robust Control of Linear Systems and nonlinear Control 1990 Birkhauser New York 447 456
    • (1990) , pp. 447-456
    • Jakubcyk, B.1    Respondek, W.2
  • 45
    • 0024607453 scopus 로고
    • “Stabilization of nonlinear systems in the plane,”
    • M. Kawski “Stabilization of nonlinear systems in the plane,” Syst. Contr. Lett. 12 1989 169 175
    • (1989) Syst. Contr. Lett. , vol.12 , pp. 169-175
    • Kawski, M.1
  • 46
    • 85113044004 scopus 로고    scopus 로고
    • M. Kawski, “Homogeneous feedback laws in dimension three,” Proc. IEEE Conf. on Decision and Control , Tampa, Dec 1989, 1370–1376.
  • 48
    • 0024718108 scopus 로고
    • “A positive real condition for global stabilization of nonlinear systems,”
    • P.V. Kokotovic H.J. Sussmann “A positive real condition for global stabilization of nonlinear systems,” Systems ans Control Letters 13 1989 125 134
    • (1989) Systems ans Control Letters , vol.13 , pp. 125-134
    • Kokotovic, P.V.1    Sussmann, H.J.2
  • 49
    • 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. 24 1956 19 77 Ser 2
    • (1956) Amer. Math. Soc. Transl. , vol.24 , pp. 19-77
    • Kurzweil, J.1
  • 51
    • 0015670958 scopus 로고
    • “Nonlinear regulator theory and inverse optimal control,”
    • P.J. Moylan B.D.O. Anderson “Nonlinear regulator theory and inverse optimal control,” IEEE Transac. Automat. Contr. AC-18 1973 460 464
    • (1973) IEEE Transac. Automat. Contr. , vol.AC-18 , pp. 460-464
    • Moylan, P.J.1    Anderson, B.D.O.2
  • 52
    • 0001945369 scopus 로고
    • Stability of C∞-mappings, I, II
    • ∞-mappings, I, II Ann. Math. 87 1962 89 104 89(1969), 254–291
    • (1962) Ann. Math. , vol.87 , pp. 89-104
    • Mather, J.N.1
  • 53
    • 85113048752 scopus 로고    scopus 로고
    • R. Marino, “High-gain stabilization and partial feedback stabilization,” 25th IEEE Conference on Decision and Control , (1986), 209–213.
  • 54
    • 0022523949 scopus 로고
    • “On the largest feedback linearizable subsystem”
    • R. Marino “On the largest feedback linearizable subsystem” Systems and Control Letters 6 1986 345 352
    • (1986) Systems and Control Letters , vol.6 , pp. 345-352
    • Marino, R.1
  • 55
    • 85113074599 scopus 로고
    • J.E. Marsden M. McCracken The Hopf Bifurcation Theorem and its Applications 1976 Springer Verlag New York
    • (1976)
    • Marsden, J.E.1    McCracken, M.2
  • 56
    • 0016093490 scopus 로고
    • “Implications of passivity in a class of nonlinear systems,”
    • P.J. Moylan “Implications of passivity in a class of nonlinear systems,” IEEE Transac. Automat. Contr. AC-19 1974 373 381
    • (1974) IEEE Transac. Automat. Contr. , vol.AC-19 , pp. 373-381
    • Moylan, P.J.1
  • 57
    • 85113075366 scopus 로고    scopus 로고
    • L. Rosier, “Homogeneous Lyapunov functions for homogeneous continuos vector field,” (preprint)
  • 58
    • 85113060352 scopus 로고    scopus 로고
    • L. Praly, B. d'Andrea-Novell and J. M. Coron, “Lyapunov design fo stabilizing controllers,” 28th IEEE Conference on Decision and Control , 1989, 1047–1052.
  • 59
    • 0343120991 scopus 로고
    • “Stability properties of autonomous homogeneous polynomial differential systems,”
    • N. Samardzija “Stability properties of autonomous homogeneous polynomial differential systems,” J. Differential Eq. 48 1983 60 70
    • (1983) J. Differential Eq. , vol.48 , pp. 60-70
    • Samardzija, N.1
  • 60
    • 0024717674 scopus 로고
    • “A universal construction of Artstein's theorem on nonlinear stabilization,”
    • E.D. Sontag “A universal construction of Artstein's theorem on nonlinear stabilization,” Systems and Control Letters 13 1989 117 123
    • (1989) Systems and Control Letters , vol.13 , pp. 117-123
    • Sontag, E.D.1
  • 61
    • 0001868633 scopus 로고
    • “Feedback stabilization of nonlinear systems,”
    • E.D. Sontag “Feedback stabilization of nonlinear systems,” M.A. Kaashoek J.H. van Schuppen A.C.M. Ran Robust Control of Linear and Nonlinear systems 1990 Birkhauser Boston
    • (1990)
    • Sontag, E.D.1
  • 62
    • 0025419843 scopus 로고
    • “Further facts about input to state stabilization,”
    • E.D. Sontag “Further facts about input to state stabilization,” IEEE Trans. Automat. Contr. AC-35 1990 473 477
    • (1990) IEEE Trans. Automat. Contr. , vol.AC-35 , pp. 473-477
    • Sontag, E.D.1
  • 63
    • 85113071712 scopus 로고
    • E.H. Spanier Algebraic Topology 1966 McGraw Hill New York
    • (1966)
    • Spanier, E.H.1
  • 64
    • 85113053352 scopus 로고    scopus 로고
    • E.D. Sontag and H.J. Sussmann, “Remarks on continuous feedback,” Proc. IEEE Conf. Decision and Control , Albuquerque, (1980), 916–921.
  • 65
    • 0024640866 scopus 로고
    • “Further comments on the stabilizability of the angular velocity of a rigid body,”
    • E.D. Sontag H.J. Sussmann “Further comments on the stabilizability of the angular velocity of a rigid body,” Systems and Control Letters 12 1989 213 217
    • (1989) Systems and Control Letters , vol.12 , pp. 213-217
    • Sontag, E.D.1    Sussmann, H.J.2
  • 66
    • 0002967668 scopus 로고
    • “ Subanalytic sets and feedback control,”
    • H.J. Sussmann “ Subanalytic sets and feedback control,” J. Differential Equations 31 1979 31 52
    • (1979) J. Differential Equations , vol.31 , pp. 31-52
    • Sussmann, H.J.1
  • 67
    • 0002425691 scopus 로고
    • Singularities of differentiable mappings
    • R. Thom H. Levine Singularities of differentiable mappings Lecture Notes in Math 1971 Springer Verlag NY 192
    • (1971) , pp. 192
    • Thom, R.1    Levine, H.2
  • 69
    • 0026118633 scopus 로고
    • “Existence of Control Lyapunov Functions and Applications to State Feedback Stabilizability of Nonlinear Systems,”
    • J. Tsinias “Existence of Control Lyapunov Functions and Applications to State Feedback Stabilizability of Nonlinear Systems,” SIAM J. Contr. Optimiz. 29 1991 457 473
    • (1991) SIAM J. Contr. Optimiz. , vol.29 , pp. 457-473
    • Tsinias, J.1
  • 70
    • 0025521044 scopus 로고
    • “Optimal Controllers and output feedback stabilization,”
    • J. Tsinias “Optimal Controllers and output feedback stabilization,” Systems and Control Letters 15 1990 277 284
    • (1990) Systems and Control Letters , vol.15 , pp. 277-284
    • Tsinias, J.1
  • 71
    • 0026118633 scopus 로고
    • “Remarks on feedback stabilizability of homogeneous systems,”
    • J. Tsinias “Remarks on feedback stabilizability of homogeneous systems,” Control - Theory and Advanced Technology 29 1991 457 473
    • (1991) Control - Theory and Advanced Technology , vol.29 , pp. 457-473
    • Tsinias, J.1
  • 72
    • 0019049056 scopus 로고
    • “Decomposition techniques for large scale systems with nonadditive interactions: stability and stabilizability,”
    • M. Vidyasagar “Decomposition techniques for large scale systems with nonadditive interactions: stability and stabilizability,” IEEE Tansac. Automat. Contr. AC-25 1980 773 779
    • (1980) IEEE Tansac. Automat. Contr. , vol.AC-25 , pp. 773-779
    • Vidyasagar, M.1
  • 73
    • 85113037939 scopus 로고    scopus 로고
    • J. C. Willems, “Dissipative dynamical systems, part I: general theory,” Arch. Rational Mech. Anal. , 45, 321–351.


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