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Volumn 65, Issue 1, 2014, Pages 74-80

Contraction theory on Riemannian manifolds

Author keywords

Contraction theory; Differential geometric methods; Incremental stability; Nonlinear control

Indexed keywords

CONTRACTION THEORY; DIFFERENTIAL GEOMETRIC METHOD; FEEDBACK INTERCONNECTION; INCREMENTAL STABILITY; NON LINEAR CONTROL; RIEMANNIAN MANIFOLD; SCIENTIFIC DISCIPLINE; STABILITY PROPERTIES;

EID: 84893315317     PISSN: 01676911     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sysconle.2013.12.016     Document Type: Article
Times cited : (90)

References (49)
  • 1
    • 0032094219 scopus 로고    scopus 로고
    • On contraction analysis for non-linear systems
    • PII S0005109898000193
    • W. Lohmiller, and J.-J.E. Slotine On contraction analysis for non-linear systems Automatica 34 6 1998 683 696 (Pubitemid 128400392)
    • (1998) Automatica , vol.34 , Issue.6 , pp. 683-696
    • Lohmiller, W.1    Slotine, J.-J.E.2
  • 2
    • 79551555317 scopus 로고    scopus 로고
    • A graphical approach to prove contraction of nonlinear circuits and systems
    • G. Russo, M. Di Bernardo, and J.-J.E. Slotine A graphical approach to prove contraction of nonlinear circuits and systems IEEE Trans. Circuits Syst. I 58 2 2011 336 348
    • (2011) IEEE Trans. Circuits Syst. i , vol.58 , Issue.2 , pp. 336-348
    • Russo, G.1    Di Bernardo, M.2    Slotine, J.-J.E.3
  • 3
    • 84860642649 scopus 로고    scopus 로고
    • Backstepping design for incremental stability
    • M. Zamani, and P. Tabuada Backstepping design for incremental stability IEEE Trans. Automat. Control 56 9 2010 2184 2189
    • (2010) IEEE Trans. Automat. Control , vol.56 , Issue.9 , pp. 2184-2189
    • Zamani, M.1    Tabuada, P.2
  • 4
    • 27844596643 scopus 로고    scopus 로고
    • Contraction analysis of non-linear distributed systems
    • DOI 10.1080/00207170500130952
    • W. Lohmiller, and J.-J.E. Slotine Contraction analysis of non-linear distributed systems Internat. J. Control 78 9 2005 678 688 (Pubitemid 41657403)
    • (2005) International Journal of Control , vol.78 , Issue.9 , pp. 678-688
    • Lohmiller, W.1    Slotine, J.-J.E.2
  • 6
    • 77954596479 scopus 로고    scopus 로고
    • Global entrainment of transcriptional systems to periodic inputs
    • e1000739
    • G. Russo, M. Di Bernardo, and E.D. Sontag Global entrainment of transcriptional systems to periodic inputs PLoS Comput. Biol. 6 4 2010 e1000739
    • (2010) PLoS Comput. Biol. , vol.6 , Issue.4
    • Russo, G.1    Di Bernardo, M.2    Sontag, E.D.3
  • 7
    • 34047214963 scopus 로고    scopus 로고
    • Algorithmic search for contraction metrics via SOS programming
    • 1657177, Proceedings of the 2006 American Control Conference
    • E. Aylward, P.A. Parrilo, J.-J.E. Slotine, Algorithmic search for contraction metrics via SOS programming, in: American Control Conference, Minneapolis, MN, USA, 2006, pp. 3001-3006. (Pubitemid 46531278)
    • (2006) Proceedings of the American Control Conference , vol.2006 , pp. 3001-3006
    • Aylward, E.1    Parrilo, P.A.2    Slotine, J.-J.E.3
  • 8
    • 0037871940 scopus 로고    scopus 로고
    • An intrinsic observer for a class of Lagrangian systems
    • N. Aghannan, and P. Rouchon An intrinsic observer for a class of Lagrangian systems IEEE Trans. Automat. Control 48 6 2003 936 945
    • (2003) IEEE Trans. Automat. Control , vol.48 , Issue.6 , pp. 936-945
    • Aghannan, N.1    Rouchon, P.2
  • 9
    • 84856417274 scopus 로고    scopus 로고
    • Symbolic models for nonlinear control systems without stability assumptions
    • M. Zamani, G. Pola, M. Mazo Jr, and P. Tabuada Symbolic models for nonlinear control systems without stability assumptions IEEE Trans. Automat. Control 57 7 2012 1804 1809
    • (2012) IEEE Trans. Automat. Control , vol.57 , Issue.7 , pp. 1804-1809
    • Zamani, M.1    Pola, G.2    Mazo, Jr.M.3    Tabuada, P.4
  • 11
    • 78149348816 scopus 로고    scopus 로고
    • A tutorial on incremental stability analysis using contraction theory
    • J. Jouffroy, and T.I. Fossen A tutorial on incremental stability analysis using contraction theory Model. Identif. Control 31 3 2010 93 106
    • (2010) Model. Identif. Control , vol.31 , Issue.3 , pp. 93-106
    • Jouffroy, J.1    Fossen, T.I.2
  • 13
    • 12244287257 scopus 로고
    • Metric properties of differential equations
    • D.C. Lewis Metric properties of differential equations Amer. J. Math. 71 2 1949 294 312
    • (1949) Amer. J. Math. , vol.71 , Issue.2 , pp. 294-312
    • Lewis, D.C.1
  • 14
    • 0012145669 scopus 로고
    • Differential equations referred to a variable metric
    • D.C. Lewis Differential equations referred to a variable metric Amer. J. Math. 73 1 1951 48 58
    • (1951) Amer. J. Math. , vol.73 , Issue.1 , pp. 48-58
    • Lewis, D.C.1
  • 15
    • 12244286552 scopus 로고
    • Sur la stabilité asymptotique des solutions d'un système d'équations différentielles
    • Z. Opial Sur la stabilité asymptotique des solutions d'un système d'équations différentielles Ann. Polon. Math. 7 1960 259 267
    • (1960) Ann. Polon. Math. , vol.7 , pp. 259-267
    • Opial, Z.1
  • 16
    • 0012184302 scopus 로고
    • On stability in the large for systems of ordinary differential equations
    • P. Hartman On stability in the large for systems of ordinary differential equations Canad. J. Math. 13 1962 480 492
    • (1962) Canad. J. Math. , vol.13 , pp. 480-492
    • Hartman, P.1
  • 17
    • 84893291940 scopus 로고
    • Dissipativity of a nonlinear system of differential equations
    • B.P. Demidovich Dissipativity of a nonlinear system of differential equations Uspekhi Mat. Nauk 16 3(99) 1961 216
    • (1961) Uspekhi Mat. Nauk , vol.16 , Issue.399 , pp. 216
    • Demidovich, B.P.1
  • 20
    • 0036493650 scopus 로고    scopus 로고
    • A Lyapunov approach to incremental stability properties
    • DOI 10.1109/9.989067, PII S0018928602028192
    • D. Angeli A Lyapunov approach to incremental stability properties IEEE Trans. Automat. Control 47 3 2002 410 421 (Pubitemid 34536795)
    • (2002) IEEE Transactions on Automatic Control , vol.47 , Issue.3 , pp. 410-421
    • Angeli, D.1
  • 21
    • 0036505787 scopus 로고    scopus 로고
    • A small-gain theorem with applications to input/output systems, incremental stability, detectability, and interconnections
    • DOI 10.1016/S0016-0032(02)00022-4, PII S0016003202000224
    • E.D. Sontag, and B. Ingalls A small-gain theorem with applications to input/output systems, incremental stability, detectability, and interconnections J. Franklin Inst. B 339 2 2002 211 229 (Pubitemid 34466874)
    • (2002) Journal of the Franklin Institute , vol.339 , Issue.2 , pp. 211-229
    • Sontag, E.D.1    Ingalls, B.2
  • 22
    • 33947407698 scopus 로고    scopus 로고
    • Analysis of interconnected oscillators by dissipativity theory
    • DOI 10.1109/TAC.2006.890471
    • G.B. Stan, and R. Sepulchre Analysis of interconnected oscillators by dissipativity theory IEEE Trans. Automat. Control 52 2 2007 256 270 (Pubitemid 46444280)
    • (2007) IEEE Transactions on Automatic Control , vol.52 , Issue.2 , pp. 256-270
    • Stan, G.-B.1    Sepulchre, R.2
  • 23
    • 67649592743 scopus 로고    scopus 로고
    • Further results on incremental input-to-state stability
    • D. Angeli Further results on incremental input-to-state stability IEEE Trans. Automat. Control 54 6 2009 1386 1391
    • (2009) IEEE Trans. Automat. Control , vol.54 , Issue.6 , pp. 1386-1391
    • Angeli, D.1
  • 25
    • 0001761833 scopus 로고
    • Functional analysis applied to nonlinear feedback systems
    • G. Zames Functional analysis applied to nonlinear feedback systems IEEE Trans. Circuit Theory 10 3 1963 392 404
    • (1963) IEEE Trans. Circuit Theory , vol.10 , Issue.3 , pp. 392-404
    • Zames, G.1
  • 28
    • 12344327544 scopus 로고    scopus 로고
    • On partial contraction analysis for coupled nonlinear oscillators
    • DOI 10.1007/s00422-004-0527-x
    • W. Wang, and J.-J.E. Slotine On partial contraction analysis for coupled nonlinear oscillators Biol. Cybernet. 92 1 2005 38 53 (Pubitemid 40134701)
    • (2005) Biological Cybernetics , vol.92 , Issue.1 , pp. 38-53
    • Wang, W.1    Slotine, J.-J.E.2
  • 29
    • 67649249972 scopus 로고    scopus 로고
    • Cooperative robot control and concurrent synchronization of Lagrangian systems
    • S.-J. Chung, and J.-J.E. Slotine Cooperative robot control and concurrent synchronization of Lagrangian systems IEEE Trans. Robot. 25 3 2009 686 700
    • (2009) IEEE Trans. Robot. , vol.25 , Issue.3 , pp. 686-700
    • Chung, S.-J.1    Slotine, J.-J.E.2
  • 30
    • 79960723494 scopus 로고    scopus 로고
    • Riemannian obsevers for Euler-Lagrange systems
    • Prague, Czech Republic
    • D.A. Ansini, J. Hamberg, Riemannian obsevers for Euler-Lagrange systems, in: IFAC World Congress, Prague, Czech Republic, 2005.
    • (2005) IFAC World Congress
    • Ansini, D.A.1    Hamberg, J.2
  • 32
    • 0034187420 scopus 로고    scopus 로고
    • Control system design for mechanical systems using contraction theory
    • W. Lohmiller, and J.-J.E. Slotine Control system design for mechanical systems using contraction theory IEEE Trans. Automat. Control 45 5 2000 984 989
    • (2000) IEEE Trans. Automat. Control , vol.45 , Issue.5 , pp. 984-989
    • Lohmiller, W.1    Slotine, J.-J.E.2
  • 37
    • 0004226864 scopus 로고
    • third ed. International Series in Pure and Applied Mathematics McGraw-Hill
    • W. Rudin Principles of Mathematical Analysis third ed. International Series in Pure and Applied Mathematics 1976 McGraw-Hill
    • (1976) Principles of Mathematical Analysis
    • Rudin, W.1
  • 38
    • 0004341311 scopus 로고
    • Interscience Tracts in Pure and Applied Mathematics Interscience Publishers New York
    • S. Kobayashi, and K. Nomizu Foundations of Differential Geometry. Vol. I Interscience Tracts in Pure and Applied Mathematics vol. 15 1963 Interscience Publishers New York
    • (1963) Foundations of Differential Geometry. Vol. i , vol.15 VOL.
    • Kobayashi, S.1    Nomizu, K.2
  • 40
    • 10244238527 scopus 로고    scopus 로고
    • Nonlinear systems: Analysis, stability and control
    • Springer
    • S.S. Sastry Nonlinear systems: analysis, stability and control Interdisciplinary Applied Mathematics vol. 10 1999 Springer
    • (1999) Interdisciplinary Applied Mathematics , vol.10 VOL.
    • Sastry, S.S.1
  • 41
    • 0346676588 scopus 로고    scopus 로고
    • A topological obstruction to continuous global stabilization of rotational motion and the unwinding phenomenon
    • S.P. Bhat, and D.S. Bernstein A topological obstruction to continuous global stabilization of rotational motion and the unwinding phenomenon Systems Control Lett. 39 1 2000 63 70
    • (2000) Systems Control Lett. , vol.39 , Issue.1 , pp. 63-70
    • Bhat, S.P.1    Bernstein, D.S.2
  • 42
  • 43
    • 0003548726 scopus 로고    scopus 로고
    • Introduction to applied nonlinear dynamic systems and chaos
    • second ed. Springer
    • S. Wiggins Introduction to applied nonlinear dynamic systems and chaos Texts in Applied Mathematics second ed. 2003 Springer
    • (2003) Texts in Applied Mathematics
    • Wiggins, S.1
  • 44
    • 0001034066 scopus 로고    scopus 로고
    • Monotone vector fields
    • S.Z. Németh Monotone vector fields Publ. Math. Debrecen 54 3-4 1999 437 449
    • (1999) Publ. Math. Debrecen , vol.54 , Issue.34 , pp. 437-449
    • Németh, S.Z.1
  • 46
    • 58149188324 scopus 로고    scopus 로고
    • Invariant monotone vector fields on Riemannian manifolds
    • A. Barani, and M.R. Pouryayevali Invariant monotone vector fields on Riemannian manifolds Nonlinear Anal. TMA 70 5 2009 1850 1861
    • (2009) Nonlinear Anal. TMA , vol.70 , Issue.5 , pp. 1850-1861
    • Barani, A.1    Pouryayevali, M.R.2
  • 48
    • 0034916151 scopus 로고    scopus 로고
    • A dual to Lyapunov's stability theorem
    • DOI 10.1016/S0167-6911(00)00087-6, PII S0167691100000876
    • A. Rantzer A dual to Lyapunov's stability theorem Systems Control Lett. 42 3 2001 161 168 (Pubitemid 32663820)
    • (2001) Systems and Control Letters , vol.42 , Issue.3 , pp. 161-168
    • Rantzer, A.1
  • 49


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.