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Volumn 17, Issue 2, 2005, Pages 101-127

Geometric homogeneity with applications to finite-time stability

Author keywords

Finite time stability; Geometric homogeneity; Homogeneous systems; Lyapunov theory; Stability

Indexed keywords

CLOSED LOOP CONTROL SYSTEMS; COMPUTATIONAL GEOMETRY; DIFFERENTIAL EQUATIONS; FEEDBACK CONTROL; FUNCTIONS; LINEAR CONTROL SYSTEMS; LINEARIZATION; LYAPUNOV METHODS; THEOREM PROVING; VECTORS;

EID: 21344471250     PISSN: 09324194     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00498-005-0151-x     Document Type: Article
Times cited : (1495)

References (47)
  • 4
    • 0032070908 scopus 로고    scopus 로고
    • Continuous, finite-time stabilization of the translational and rotational double integrators
    • Bhat SP, Bernstein DS (1998) Continuous, finite-time stabilization of the translational and rotational double integrators. IEEE Trans Automatic Control 43:678-682
    • (1998) IEEE Trans. Automatic Control , vol.43 , pp. 678-682
    • Bhat, S.P.1    Bernstein, D.S.2
  • 5
    • 0000761428 scopus 로고    scopus 로고
    • Finite-time stability of continuous autonomous systems
    • Bhat SP, Bernstein DS (2000) Finite-time stability of continuous autonomous systems. SIAM J Control Optim 38:751-766
    • (2000) SIAM J. Control Optim. , vol.38 , pp. 751-766
    • Bhat, S.P.1    Bernstein, D.S.2
  • 6
    • 0038351240 scopus 로고
    • Local semi-dynamical systems
    • Springer, Berlin Heidelberg New York
    • Bhatia NP, Hajek O (1969) Local semi-dynamical systems. Lecture Notes in Mathematics, vol 90. Springer, Berlin Heidelberg New York
    • (1969) Lecture Notes in Mathematics , vol.90
    • Bhatia, N.P.1    Hajek, O.2
  • 8
    • 21344448601 scopus 로고
    • Asymptotic stability in 3-space
    • Cesari L, LaSalle J, Lefschetz S (eds) Princeton University Press
    • Coleman C (1960) Asymptotic stability in 3-space. In: Cesari L, LaSalle J, Lefschetz S (eds) Contributions to the theory of nonlinear oscillations, vol V. Princeton University Press, pp 257-268
    • (1960) Contributions to the Theory of Nonlinear Oscillations , vol.5 , pp. 257-268
    • Coleman, C.1
  • 9
    • 0024931884 scopus 로고
    • Some sufficient conditions for the asymptotic stabilizability of three dimensional homogeneous polynomial systems
    • Tampa
    • Dayawansa WP, Martin CF (1989) Some sufficient conditions for the asymptotic stabilizability of three dimensional homogeneous polynomial systems. In: Proceedings of conference on decision and control. Tampa, pp 1366-1369
    • (1989) Proceedings of Conference on Decision and Control , pp. 1366-1369
    • Dayawansa, W.P.1    Martin, C.F.2
  • 11
  • 12
    • 84904780282 scopus 로고
    • Designing a bounded control of dynamic systems in entire space with the aid of controllability function
    • Gavrilyako VM, Korobov VI, Skylar GM (1986) Designing a bounded control of dynamic systems in entire space with the aid of controllability function. Automation Remote Control 47:1484-1490
    • (1986) Automation Remote Control , vol.47 , pp. 1484-1490
    • Gavrilyako, V.M.1    Korobov, V.I.2    Skylar, G.M.3
  • 13
    • 0003980507 scopus 로고
    • Springer, Berlin Heidelberg New York
    • Hahn W (1967) Stability of motion. Springer, Berlin Heidelberg New York
    • (1967) Stability of Motion
    • Hahn, W.1
  • 14
    • 0022751616 scopus 로고
    • Finite time controllers
    • Haimo VT (1986) Finite time controllers. SIAM J Control Optim. 24:760-770
    • (1986) SIAM J. Control Optim. , vol.24 , pp. 760-770
    • Haimo, V.T.1
  • 15
    • 0003826524 scopus 로고
    • Ordinary Differential Equations
    • 2nd edn. Birkhäuser, Boston
    • Hartman P (1982) Ordinary differential equations. 2nd edn. Birkhäuser, Boston
    • (1982)
    • Hartman, P.1
  • 16
    • 0001110408 scopus 로고
    • Homogeneous coordinates and continuous asymptotically stabilizing feedback controls
    • Elaydi S (ed) Lecture Notes in Pure and Applied Mathematics Marcel Dekker, New York
    • Hermes H (1991) Homogeneous coordinates and continuous asymptotically stabilizing feedback controls. In: Elaydi S (ed) Differential equations, stability and control. Lecture Notes in Pure and Applied Mathematics, vol 127. Marcel Dekker, New York, pp 249-260
    • (1991) Differential Equations, Stability and Control , vol.127 , pp. 249-260
    • Hermes, H.1
  • 17
    • 0026173040 scopus 로고
    • Nilpotent and high-order approximations of vector field systems
    • Hermes H (1991) Nilpotent and high-order approximations of vector field systems. SIAM Rev 33:238-264
    • (1991) SIAM Rev. , vol.33 , pp. 238-264
    • Hermes, H.1
  • 18
    • 21344470849 scopus 로고
    • Vector field approximations; flow homogeneity
    • Wiener J, Hale JK (eds) Longman Sci Tech
    • Hermes H (1992) Vector field approximations; flow homogeneity. In: Wiener J, Hale JK (eds) Ordinary and delay differential equations. Longman Sci Tech, pp 80-89
    • (1992) Ordinary and Delay Differential Equations , pp. 80-89
    • Hermes, H.1
  • 19
    • 0029639910 scopus 로고
    • Homogeneous feedback controls for homogeneous systems
    • Hermes H (1995) Homogeneous feedback controls for homogeneous systems. Syst Control Lett 24:7-11
    • (1995) Syst. Control Lett. , vol.24 , pp. 7-11
    • Hermes, H.1
  • 20
    • 0037162403 scopus 로고    scopus 로고
    • Finite-time stabilization and stabilizability of a class of controllable systems
    • Hong Y (2002) Finite-time stabilization and stabilizability of a class of controllable systems. Systems Control Lett 46:231-236
    • (2002) Systems Control Lett. , vol.46 , pp. 231-236
    • Hong, Y.1
  • 21
    • 0035249145 scopus 로고    scopus 로고
    • On an output feedback finite-time stabilization problem
    • Hong Y, Huang J, Xu Y (2001) On an output feedback finite-time stabilization problem. IEEE Trans Automatic Control 46:305-309
    • (2001) IEEE Trans. Automatic Control , vol.46 , pp. 305-309
    • Hong, Y.1    Huang, J.2    Xu, Y.3
  • 25
    • 21344456505 scopus 로고
    • Controllability, approximations and stabilization
    • Bowers K, Lund J (eds) Birkhäuser Boston
    • Kawski M (1988) Controllability, approximations and stabilization. In: Bowers K, Lund J (eds) Computation and control, vol 1. Birkhäuser, Boston, pp 155-167
    • (1988) Computation and Control , vol.1 , pp. 155-167
    • Kawski, M.1
  • 28
    • 0024607453 scopus 로고
    • Stabilization of nonlinear systems in the plane
    • Kawski M (1989) Stabilization of nonlinear systems in the plane. Syst Control Lett 12:169-175
    • (1989) Syst. Control Lett. , vol.12 , pp. 169-175
    • Kawski, M.1
  • 29
    • 0000575314 scopus 로고
    • Homogeneous stabilizing feedback laws
    • Kawski M (1990) Homogeneous stabilizing feedback laws. Control-Theory Adv Technol 6:497-516
    • (1990) Control-Theory Adv. Technol. , vol.6 , pp. 497-516
    • Kawski, M.1
  • 30
    • 0344952645 scopus 로고
    • Families of dilations and asymptotic stability
    • Bonnard B, Bride B, Gauthier JP, Kupka I (eds) Birkhäuser, Boston
    • Kawski M (1991) Families of dilations and asymptotic stability. In: Bonnard B, Bride B, Gauthier JP, Kupka I (eds) Analysis of controlled dynamical systems, progress in systems and control theory, vol 8. Birkhäuser, Boston, pp 285-294
    • (1991) Analysis of Controlled Dynamical Systems, Progress in Systems and Control Theory , vol.8 , pp. 285-294
    • Kawski, M.1
  • 31
    • 21344471086 scopus 로고    scopus 로고
    • Geometric homogeneity and stabilization
    • Krener A, Mayne D (eds) Elsevier. Amsterdam
    • Kawski M (1999) Geometric homogeneity and stabilization. In: Krener A, Mayne D (eds) IFAC postprint volumes series. Elsevier. Amsterdam
    • (1999) IFAC Postprint Volumes Series
    • Kawski, M.1
  • 32
    • 0004178386 scopus 로고    scopus 로고
    • 2nd edn. Prentice-Hall, Upper Saddle River
    • Khalil HK (1996) Nonlinear systems. 2nd edn. Prentice-Hall, Upper Saddle River
    • (1996) Nonlinear Systems
    • Khalil, H.K.1
  • 33
    • 84904781543 scopus 로고
    • Design of constrained controls for linear systems
    • Komarov VA (1984) Design of constrained controls for linear systems. Automation Remote Control 45:1280-1286
    • (1984) Automation Remote Control , vol.45 , pp. 1280-1286
    • Komarov, V.A.1
  • 34
    • 0031145089 scopus 로고    scopus 로고
    • Exponential stabilization of driftless nonlinear control systems using homogeneous feedback
    • M'Closkey RT, Murray RM (1997) Exponential stabilization of driftless nonlinear control systems using homogeneous feedback. IEEE Trans Automatic Control 42:614-628
    • (1997) IEEE Trans. Automatic Control , vol.42 , pp. 614-628
    • M'Closkey, R.T.1    Murray, R.M.2
  • 36
    • 0031388994 scopus 로고    scopus 로고
    • Generalized weighted homogeneity and state dependent time scale for controllable systems
    • San Diego
    • Praly L (1997) Generalized weighted homogeneity and state dependent time scale for controllable systems. In: Proceedings of conference on decision and control, San Diego pp 4342-4347
    • (1997) Proceedings of Conference on Decision and Control , pp. 4342-4347
    • Praly, L.1
  • 37
    • 0026998882 scopus 로고
    • Homogeneous Lyapunov function for homogeneous continuous vector field
    • Rosier L (1992) Homogeneous Lyapunov function for homogeneous continuous vector field. Syst Control Lett 19:467-473
    • (1992) Syst. Control Lett. , vol.19 , pp. 467-473
    • Rosier, L.1
  • 38
    • 0003826825 scopus 로고
    • Etude de quelques problèmes de stabilisation
    • PhD Thesis, Ecole Normale Supérieure de Cachan, France
    • Rosier L (1993) Etude de quelques problèmes de stabilisation. PhD Thesis, Ecole Normale Supérieure de Cachan, France
    • (1993)
    • Rosier, L.1
  • 40
    • 0004095457 scopus 로고
    • Optimal relay and saturating control system synthesis
    • Peter Peregrinus Ltd
    • Ryan EP (1982) Optimal relay and saturating control system synthesis. IEE control engineering series, vol 14. Peter Peregrinus Ltd
    • (1982) IEE Control Engineering Series , vol.14
    • Ryan, E.P.1
  • 41
    • 0026126242 scopus 로고
    • Finite-time stabilization of uncertain nonlinear planar systems
    • Ryan EP (1991) Finite-time stabilization of uncertain nonlinear planar systems. Dyn Control 1:83-94
    • (1991) Dyn. Control , vol.1 , pp. 83-94
    • Ryan, E.P.1
  • 42
    • 0029499214 scopus 로고
    • Universal stabilization of a class of nonlinear systems with homogeneous vector fields
    • Ryan EP (1995) Universal stabilization of a class of nonlinear systems with homogeneous vector fields. Syst Control Lett 26:177-184
    • (1995) Syst. Control Lett. , vol.26 , pp. 177-184
    • Ryan, E.P.1
  • 44
    • 0029747566 scopus 로고    scopus 로고
    • Homogeneous Lyapunov functions and necessary conditions for stabilization
    • Sepulchre R, Aeyels D (1996) Homogeneous Lyapunov functions and necessary conditions for stabilization. Math Control Signals Syst 9:34-58
    • (1996) Math. Control Signals Syst. , vol.9 , pp. 34-58
    • Sepulchre, R.1    Aeyels, D.2
  • 45
    • 0030243809 scopus 로고    scopus 로고
    • Stabilizability does not imply homogeneous stabilizability for controllable homogeneous systems
    • Sepulchre R, Aeyels D (1996) Stabilizability does not imply homogeneous stabilizability for controllable homogeneous systems. SIAM J Control Optimization 34:1798-1813
    • (1996) SIAM J. Control Optimization , vol.34 , pp. 1798-1813
    • Sepulchre, R.1    Aeyels, D.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.