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Volumn 22, Issue 2, 2010, Pages 155-184

Arc-length-based Lyapunov tests for convergence and stability with applications to systems having a continuum of equilibria

Author keywords

Arc length; Consensus; Continuum of equilibria; Convergence; Lyapunov stability; Semistability

Indexed keywords

ARC LENGTH; CONSENSUS; CONTINUUM OF EQUILIBRIA; CONVERGENCE; LYAPUNOV STABILITY; SEMISTABILITY;

EID: 78049467719     PISSN: 09324194     EISSN: 1435568X     Source Type: Journal    
DOI: 10.1007/s00498-010-0054-3     Document Type: Article
Times cited : (46)

References (46)
  • 1
    • 0000795196 scopus 로고
    • Singular perturbation of autonomous linear systems
    • 0413.34055 10.1137/0510051 529072
    • SL Campbell NJ Rose 1979 Singular perturbation of autonomous linear systems SIAM J Math Anal 10 542 551 0413.34055 10.1137/0510051 529072
    • (1979) SIAM J Math Anal , vol.10 , pp. 542-551
    • Campbell, S.L.1    Rose, N.J.2
  • 2
    • 0029323801 scopus 로고
    • Lyapunov stability, semistability, and asymptotic stability of matrix second-order systems
    • 10.1115/1.2838656
    • DS Bernstein SP Bhat 1995 Lyapunov stability, semistability, and asymptotic stability of matrix second-order systems ASME Trans J Vib Acoust 117 145 153 10.1115/1.2838656
    • (1995) ASME Trans J Vib Acoust , vol.117 , pp. 145-153
    • Bernstein, D.S.1    Bhat, S.P.2
  • 3
    • 4944234701 scopus 로고    scopus 로고
    • Nontangency-based Lyapunov tests for convergence and stability in systems having a continuum of equilibria
    • 1078.34031 10.1137/S0363012902407119 2046384
    • SP Bhat DS Bernstein 2003 Nontangency-based Lyapunov tests for convergence and stability in systems having a continuum of equilibria SIAM J Control Optim 42 5 1745 1775 1078.34031 10.1137/S0363012902407119 2046384
    • (2003) SIAM J Control Optim , vol.42 , Issue.5 , pp. 1745-1775
    • Bhat, S.P.1    Bernstein, D.S.2
  • 5
    • 0001364051 scopus 로고
    • The Existence and Uniqueness of Steady States for a Class of Chemical Reaction Networks
    • M Feinberg 1995 The existence and uniqueness of steady states for a class of chemical reaction networks Arch Ration Mech Anal 132 311 370 0853.92024 10.1007/BF00375614 1365832 (Pubitemid 126013836)
    • (1995) Archive for Rational Mechanics and Analysis , vol.132 , Issue.4 , pp. 311-370
    • Feinberg, M.1
  • 6
    • 0035390982 scopus 로고    scopus 로고
    • Structure and stability of certain chemical networks and applications to the kinetic proofreading model of T-cell receptor signal transduction
    • DOI 10.1109/9.935056, PII S0018928601067447
    • ED Sontag 2001 Structure and stability of certain chemical networks and applications to the kinetic proofreading model of t-cell receptor signal transduction IEEE Trans Autom Control 46 1028 1047 1049.92020 10.1109/9.935056 1842137 (Pubitemid 32732627)
    • (2001) IEEE Transactions on Automatic Control , vol.46 , Issue.7 , pp. 1028-1047
    • Sontag, E.D.1
  • 7
    • 69249171413 scopus 로고    scopus 로고
    • Modeling and analysis of mass-action kinetics: Nonnegativity, realizability, reducibility, and semistability
    • 10.1109/MCS.2009.932926 2543375
    • V Chellaboina SP Bhat WM Haddad DS Bernstein 2009 Modeling and analysis of mass-action kinetics: nonnegativity, realizability, reducibility, and semistability IEEE Control Syst Mag 29 4 60 78 10.1109/MCS.2009.932926 2543375
    • (2009) IEEE Control Syst Mag , vol.29 , Issue.4 , pp. 60-78
    • Chellaboina, V.1    Bhat, S.P.2    Haddad, W.M.3    Bernstein, D.S.4
  • 9
    • 0022080122 scopus 로고
    • Adaptive stabilization of linear systems with unknown high-frequency gain
    • 0573.93037 10.1109/TAC.1985.1104006 789325
    • DR Mudgett AS Morse 1985 Adaptive stabilization of linear systems with unknown high-frequency gain IEEE Trans Autom Control 30 6 549 554 0573.93037 10.1109/TAC.1985.1104006 789325
    • (1985) IEEE Trans Autom Control , vol.30 , Issue.6 , pp. 549-554
    • Mudgett, D.R.1    Morse, A.S.2
  • 11
    • 0004418006 scopus 로고
    • Some remarks on a conjecture in parameter adaptive control
    • 0524.93037 10.1016/0167-6911(83)90021-X 722952
    • RD Nussbaum 1983 Some remarks on a conjecture in parameter adaptive control Syst Control Lett 3 243 246 0524.93037 10.1016/0167-6911(83)90021-X 722952
    • (1983) Syst Control Lett , vol.3 , pp. 243-246
    • Nussbaum, R.D.1
  • 13
    • 4644244041 scopus 로고    scopus 로고
    • Consensus problems in networks of agents with switching topology and time-delays
    • 10.1109/TAC.2004.834113 2086916
    • R Olfati-Saber RM Murray 2004 Consensus problems in networks of agents with switching topology and time-delays IEEE Trans Autom Control 49 9 1520 1533 10.1109/TAC.2004.834113 2086916
    • (2004) IEEE Trans Autom Control , vol.49 , Issue.9 , pp. 1520-1533
    • Olfati-Saber, R.1    Murray, R.M.2
  • 14
    • 34548265220 scopus 로고    scopus 로고
    • Passivity as a design tool for group coordination
    • DOI 10.1109/TAC.2007.902733
    • M Arcak 2007 Passivity as a design tool for group coordination IEEE Trans Autom Control 52 8 1380 1390 10.1109/TAC.2007.902733 2341743 (Pubitemid 47321551)
    • (2007) IEEE Transactions on Automatic Control , vol.52 , Issue.8 , pp. 1380-1390
    • Arcak, M.1
  • 15
    • 54049150392 scopus 로고    scopus 로고
    • Finite-time semistability and consensus for nonlinear dynamical networks
    • 10.1109/TAC.2008.929392 2454755
    • Q Hui WM Haddad SP Bhat 2008 Finite-time semistability and consensus for nonlinear dynamical networks IEEE Trans Autom Control 53 8 1887 1900 10.1109/TAC.2008.929392 2454755
    • (2008) IEEE Trans Autom Control , vol.53 , Issue.8 , pp. 1887-1900
    • Hui, Q.1    Haddad, W.M.2    Bhat, S.P.3
  • 16
    • 0024909476 scopus 로고
    • Convergent activation dynamics in continuous time networks
    • DOI 10.1016/0893-6080(89)90018-X
    • M Hirsch 1989 Convergent activation dynamics in continuous time networks Neural Netw 2 331 349 10.1016/0893-6080(89)90018-X (Pubitemid 20609006)
    • (1989) Neural Networks , vol.2 , Issue.5 , pp. 331-349
    • Hirsch Morris, W.1
  • 17
    • 10944255986 scopus 로고    scopus 로고
    • Absolute stability of analytic neural networks: An approach based on finite trajectory length
    • DOI 10.1109/TCSI.2004.838143
    • M Forti A Tesi 2004 Absolute stability of analytic neural networks: an approach based on finite trajectory length IEEE Trans Circuits Syst I 51 12 2460 2469 10.1109/TCSI.2004.838143 2104662 (Pubitemid 40009467)
    • (2004) IEEE Transactions on Circuits and Systems I: Regular Papers , vol.51 , Issue.12 , pp. 2460-2469
    • Forti, M.1    Tesi, A.2
  • 18
    • 33646735617 scopus 로고    scopus 로고
    • Convergence of the iterates of descent methods for analytic cost functions
    • 1092.90036 10.1137/040605266 2197994
    • P-A Absil R Mahony B Andrews 2005 Convergence of the iterates of descent methods for analytic cost functions SIAM J Optim 16 2 531 547 1092.90036 10.1137/040605266 2197994
    • (2005) SIAM J Optim , vol.16 , Issue.2 , pp. 531-547
    • Absil, P.-A.1    Mahony, R.2    Andrews, B.3
  • 20
    • 0010944411 scopus 로고
    • Sur les trajectoires du gradient d'une fonction analytique
    • Dipartimento di Matematica, Istituto di Geometria, Università di Bologna, Bologna, Italy
    • Łojasiewicz S (1984) Sur les trajectoires du gradient d'une fonction analytique. In: Seminari di Geometria 1982-1983. Dipartimento di Matematica, Istituto di Geometria, Università di Bologna, Bologna, Italy, pp 115-117
    • (1984) Seminari di Geometria 1982-1983 , pp. 115-117
    • Łojasiewicz, S.1
  • 21
    • 0034310138 scopus 로고    scopus 로고
    • Proof of the gradient conjecture of R. Thom
    • 1053.37008 10.2307/2661354
    • K Kurdyka T Mostowski A Parusiński 2000 Proof of the gradient conjecture of R. Thom Ann Math 152 763 792 1053.37008 10.2307/2661354
    • (2000) Ann Math , vol.152 , pp. 763-792
    • Kurdyka, K.1    Mostowski, T.2    Parusiński, A.3
  • 22
    • 33748133454 scopus 로고    scopus 로고
    • On the stable equilibrium points of gradient systems
    • DOI 10.1016/j.sysconle.2006.01.002, PII S0167691106000107
    • P-A Absil K Kurdyka 2006 On the stable equilibrium points of gradient systems Syst Control Lett 55 573 577 1129.34320 10.1016/j.sysconle.2006.01.002 2225367 (Pubitemid 44308178)
    • (2006) Systems and Control Letters , vol.55 , Issue.7 , pp. 573-577
    • Absil, P.-A.1    Kurdyka, K.2
  • 23
    • 35248817843 scopus 로고    scopus 로고
    • Pointwise convergence of gradient-like systems
    • 1130.37012 10.1002/mana.200410564 2354979
    • C Lageman 2007 Pointwise convergence of gradient-like systems Math Nachr 280 13-14 1543 1558 1130.37012 10.1002/mana.200410564 2354979
    • (2007) Math Nachr , vol.280 , Issue.1314 , pp. 1543-1558
    • Lageman, C.1
  • 24
    • 37849187126 scopus 로고    scopus 로고
    • Convergence of neural networks for programming problems via a nonsmooth Łojasiewicz inequality
    • DOI 10.1109/TNN.2006.879775
    • M Forti P Nistri M Quincampoix 2006 Convergence of neural networks for programming problems via a nonsmooth Łojasiewicz inequality IEEE Trans Neural Netw 17 6 1471 1486 10.1109/TNN.2006.879775 (Pubitemid 44824261)
    • (2006) IEEE Transactions on Neural Networks , vol.17 , Issue.6 , pp. 1471-1486
    • Forti, M.1    Nistri, P.2    Quincampoix, M.3
  • 25
    • 36249023228 scopus 로고    scopus 로고
    • The Łojasiewicz inequality for nonsmooth subanalytic functions with applications to subgradient dynamical systems
    • 1129.26012 10.1137/050644641 2274510
    • J Bolte A Daniilidis A Lewis 2007 The Łojasiewicz inequality for nonsmooth subanalytic functions with applications to subgradient dynamical systems SIAM J Optim 17 4 1205 1223 1129.26012 10.1137/050644641 2274510
    • (2007) SIAM J Optim , vol.17 , Issue.4 , pp. 1205-1223
    • Bolte, J.1    Daniilidis, A.2    Lewis, A.3
  • 26
    • 0038351240 scopus 로고
    • Local semi-dynamical systems
    • Springer-Verlag, Berlin
    • Bhatia NP, Hajek O (1969) Local semi-dynamical systems. In: Lecture notes in mathematics, vol 90. Springer-Verlag, Berlin
    • (1969) Lecture Notes in Mathematics , vol.90
    • Bhatia, N.P.1    Hajek, O.2
  • 27
    • 0030414465 scopus 로고    scopus 로고
    • Semidefinite Lyapunov functions stability and stabilization
    • 0868.93048 10.1007/BF01211748 1418816
    • A Iggidr B Kalitine R Outbib 1996 Semidefinite Lyapunov functions stability and stabilization Math Control Signal Syst 9 95 106 0868.93048 10.1007/BF01211748 1418816
    • (1996) Math Control Signal Syst , vol.9 , pp. 95-106
    • Iggidr, A.1    Kalitine, B.2    Outbib, R.3
  • 28
    • 0142184076 scopus 로고    scopus 로고
    • Arc-length-based Lyapunov tests for convergence and stability in systems having a continuum of equilibria
    • Denver, CO, June 2003
    • Bhat SP, Bernstein DS (2003) Arc-length-based Lyapunov tests for convergence and stability in systems having a continuum of equilibria. In: Proceedings of American control conference, Denver, CO, June 2003, pp 2961-2966
    • (2003) Proceedings of American Control Conference , pp. 2961-2966
    • Bhat, S.P.1    Bernstein, D.S.2
  • 36
    • 33646976814 scopus 로고
    • Some extensions of Liapunov's second method
    • 118902
    • JP LaSalle 1960 Some extensions of Liapunov's second method IRE Trans Circuit Theory CT-7 4 520 527 118902
    • (1960) IRE Trans Circuit Theory , vol.7 , Issue.4 , pp. 520-527
    • Lasalle, J.P.1
  • 37
    • 0029321632 scopus 로고
    • An integral-invariance principle for nonlinear systems
    • 0831.93058 10.1109/9.388676 1345955
    • CI Byrnes CF Martin 1995 An integral-invariance principle for nonlinear systems IEEE Trans Autom Control 40 983 994 0831.93058 10.1109/9.388676 1345955
    • (1995) IEEE Trans Autom Control , vol.40 , pp. 983-994
    • Byrnes, C.I.1    Martin, C.F.2
  • 38
    • 0036041249 scopus 로고    scopus 로고
    • Integral characterizations of uniform asymptotic and exponential stability with applications
    • DOI 10.1007/s004980200007
    • A Teel E Panteley A Loría 2002 Integral characterizations of uniform asymptotic and exponential stability with applications Math Control Signal Syst 15 177 201 1015.93055 10.1007/s004980200007 (Pubitemid 34993178)
    • (2002) Mathematics of Control, Signals, and Systems , vol.15 , Issue.3 , pp. 177-201
    • Teel, A.1    Panteley, E.2    Loria, A.3
  • 42
    • 0001215663 scopus 로고
    • Asymptotic stability and feedback stabilization
    • R.S. Millman R.W. Brockett H.J. Sussmann (eds). Birkhäuser Boston
    • Brockett RW (1983) Asymptotic stability and feedback stabilization. In: Millman RS, Brockett RW, Sussmann HJ (eds) Differential geometric control theory. Birkhäuser, Boston, pp 181-191
    • (1983) Differential Geometric Control Theory , pp. 181-191
    • Brockett, R.W.1
  • 46
    • 0004267646 scopus 로고
    • Princeton University Press Princeton 0193.18401
    • Rockafellar RT (1970) Convex analysis. Princeton University Press, Princeton
    • (1970) Convex Analysis
    • Rockafellar, R.T.1


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