메뉴 건너뛰기




Volumn 55, Issue 4, 2010, Pages 841-854

Strict lyapunov function constructions under lasalle conditions with an application to lotka-volterra systems

Author keywords

Biological systems; LaSalle conditions; Lyapunov function

Indexed keywords

DEATH RATES; LASALLE CONDITIONS; LOTKA-VOLTERRA; LOTKA-VOLTERRA MODELS; LOTKA-VOLTERRA SYSTEMS; LYAPUNOV; LYAPUNOV FUNCTION CONSTRUCTIONS; TIME VARYING;

EID: 77950844773     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2010.2041995     Document Type: Article
Times cited : (26)

References (21)
  • 1
    • 0033165467 scopus 로고    scopus 로고
    • Input-to-state stability of PD-controlled robotic systems
    • D. Angeli, "Input-to-state stability of PD-controlled robotic systems," Automatica J. IFAC, vol.35, no.7, pp. 1285-1290, 1999.
    • (1999) Automatica J. IFAC , vol.35 , Issue.7 , pp. 1285-1290
    • Angeli, D.1
  • 2
    • 14244265403 scopus 로고    scopus 로고
    • Separation principles for input-output and integral-input to state stability
    • D. Angeli, B. Ingalls, E. D. Sontag, and Y. Wang, "Separation principles for input-output and integral-input to state stability," SIAM J. Control Optim., vol.43, no.1, pp. 256-276, 2004.
    • (2004) SIAM J. Control Optim , vol.43 , Issue.1 , pp. 256-276
    • Angeli, D.1    Ingalls, B.2    Sontag, E.D.3    Wang, Y.4
  • 3
    • 0034195786 scopus 로고    scopus 로고
    • A characterization of integral input-to-state stability
    • Jun.
    • D. Angeli, E. D. Sontag, and Y. Wang, "A characterization of integral input-to-state stability," IEEE Trans. Autom. Control, vol.45, no.6, pp. 1082-1097, Jun. 2000.
    • (2000) IEEE Trans. Autom. Control , vol.45 , Issue.6 , pp. 1082-1097
    • Angeli, D.1    Sontag, E.D.2    Wang, Y.3
  • 4
    • 0002239179 scopus 로고    scopus 로고
    • Asymptotic stability and smooth Lyapunov functions
    • F. Clarke, Y. Ledyaev, and R. Stern, "Asymptotic stability and smooth Lyapunov functions," J. Diff. Eq., vol.149, no.1, pp. 69-114, 1998.
    • (1998) J. Diff. Eq , vol.149 , Issue.1 , pp. 69-114
    • Clarke, F.1    Ledyaev, Y.2    Stern, R.3
  • 5
    • 0034425490 scopus 로고    scopus 로고
    • Control Lyapunov functions for homogeneous Jurdjevic-Quinn systems
    • L. Faubourg and J.-B. Pomet, "Control Lyapunov functions for homogeneous Jurdjevic-Quinn systems," ESAIM Control Optim. Calc. Var., vol.5, pp. 293-311, 2000.
    • (2000) ESAIM Control Optim. Calc. Var , vol.5 , pp. 293-311
    • Faubourg, L.1    Pomet, J.-B.2
  • 6
    • 0000468175 scopus 로고
    • Limiting behavior for competing species
    • S. Hsu, "Limiting behavior for competing species," SIAM J. Appl. Math, vol.34, no.4, pp. 760-763, 1978.
    • (1978) SIAM J. Appl. Math , vol.34 , Issue.4 , pp. 760-763
    • Hsu, S.1
  • 7
    • 0001374626 scopus 로고
    • Controllability and stability
    • V. Jurdjevic and J. P. Quinn, "Controllability and stability," J. Diff. Eq., vol.28, no.3, pp. 381-389, 1978.
    • (1978) J. Diff. Eq , vol.28 , Issue.3 , pp. 381-389
    • Jurdjevic, V.1    Quinn, J.P.2
  • 8
    • 0004178386 scopus 로고    scopus 로고
    • Third ed. Upper Saddle River, NJ: Prentice Hall
    • H. Khalil, Nonlinear Systems, Third ed. Upper Saddle River, NJ: Prentice Hall, 2002.
    • (2002) Nonlinear Systems
    • Khalil, H.1
  • 10
    • 26244435293 scopus 로고    scopus 로고
    • A generalization of Krasovskii-LaSalle theorem for nonlinear time-varying systems: Converse results and applications
    • Aug.
    • T.-C. Lee and Z.-P. Jiang, "A generalization of Krasovskii-LaSalle theorem for nonlinear time-varying systems: Converse results and applications," IEEE Trans. Autom. Control, vol.50, no.8, pp. 1147-1163, Aug. 2005.
    • (2005) IEEE Trans. Autom. Control , vol.50 , Issue.8 , pp. 1147-1163
    • Lee, T.-C.1    Jiang, Z.-P.2
  • 11
    • 0017064938 scopus 로고
    • Limiting behavior for several interacting populations
    • A. Leung, "Limiting behavior for several interacting populations," Math. Biosci., vol.29, no.1-2, pp. 85-98, 1976.
    • (1976) Math. Biosci , vol.29 , Issue.1-2 , pp. 85-98
    • Leung, A.1
  • 12
    • 14644386858 scopus 로고    scopus 로고
    • A nested Matrosov theorem and persistency of excitation for uniform convergence in stable nonautonomous systems
    • Feb.
    • A. Loría, E. Panteley, D. Popović, and A. Teel, "A nested Matrosov theorem and persistency of excitation for uniform convergence in stable nonautonomous systems," IEEE Trans. Autom. Control, vol.50, no.2, pp. 183-198, Feb. 2005.
    • (2005) IEEE Trans. Autom. Control , vol.50 , Issue.2 , pp. 183-198
    • Loría, A.1    Panteley, E.2    Popović, D.3    Teel, A.4
  • 13
    • 33244461550 scopus 로고    scopus 로고
    • Further constructions of control-Lyapunov functions and stabilizing feedbacks for systems satisfying the Jurdjevic-Quinn conditions
    • Feb.
    • F. Mazenc and M. Malisoff, "Further constructions of control-Lyapunov functions and stabilizing feedbacks for systems satisfying the Jurdjevic-Quinn conditions," IEEE Trans. Autom. Control, vol.51, no.2, pp. 360-365, Feb. 2006.
    • (2006) IEEE Trans. Autom. Control , vol.51 , Issue.2 , pp. 360-365
    • Mazenc, F.1    Malisoff, M.2
  • 14
    • 59649110045 scopus 로고    scopus 로고
    • A simplified design for strict Lyapunov functions under Matrosov conditions
    • Jan.
    • F. Mazenc, M. Malisoff, and O. Bernard, "A simplified design for strict Lyapunov functions under Matrosov conditions," IEEE Trans. Autom. Control, vol.54, no.1, pp. 177-183, Jan. 2009.
    • (2009) IEEE Trans. Autom. Control , vol.54 , Issue.1 , pp. 177-183
    • Mazenc, F.1    Malisoff, M.2    Bernard, O.3
  • 15
    • 3042641747 scopus 로고    scopus 로고
    • Strong Lyapunov functions for systems satisfying the conditions of la Salle
    • Jun.
    • F. Mazenc and D. Nešić, "Strong Lyapunov functions for systems satisfying the conditions of La Salle," IEEE Trans. Autom. Control, vol.49, no.6, pp. 1026-1030, Jun. 2004.
    • (2004) IEEE Trans. Autom. Control , vol.49 , Issue.6 , pp. 1026-1030
    • Mazenc, F.1    Nešić, D.2
  • 16
    • 0030287289 scopus 로고    scopus 로고
    • Adding integrations, saturated controls, and stabilization for feedforward systems
    • Nov.
    • F. Mazenc and L. Praly, "Adding integrations, saturated controls, and stabilization for feedforward systems," IEEE Trans. Autom. Control, vol.41, no.11, pp. 1559-1578, Nov. 1996.
    • (1996) IEEE Trans. Autom. Control , vol.41 , Issue.11 , pp. 1559-1578
    • Mazenc, F.1    Praly, L.2
  • 17
    • 0032672053 scopus 로고    scopus 로고
    • On the stabilization of smooth nonlinear systems
    • Jan.
    • R. Outbib and J. Vivalda, "On the stabilization of smooth nonlinear systems," IEEE Trans. Autom. Control, vol.44, no.1, pp. 200-202, Jan. 1999.
    • (1999) IEEE Trans. Autom. Control , vol.44 , Issue.1 , pp. 200-202
    • Outbib, R.1    Vivalda, J.2
  • 19
    • 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," Syst. Control Lett., vol.13, no.2, pp. 117-123, 1989.
    • (1989) Syst. Control Lett , vol.13 , Issue.2 , pp. 117-123
    • Sontag, E.D.1
  • 20
    • 0348241184 scopus 로고    scopus 로고
    • Comments on integral variants of ISS
    • E. D. Sontag, "Comments on integral variants of ISS," Syst. Control Lett., vol.34, no.1-2, pp. 93-100, 1998.
    • (1998) Syst. Control Lett , vol.34 , Issue.1-2 , pp. 93-100
    • Sontag, E.D.1
  • 21
    • 47749104184 scopus 로고    scopus 로고
    • Input-to-state stability: Basic concepts and results
    • E. D. Sontag, P. Nistri and G. Stefani Eds. Berlin, Germany
    • E. D. Sontag, P. Nistri and G. Stefani, Eds., "Input-to-state stability: Basic concepts and results," in Proc. Nonlin. Optim. Control Theory. Lectures Given C.I.M.E. Summer School, Berlin, Germany, 2008, vol.1932, pp. 63-220.
    • (2008) Proc. Nonlin. Optim. Control Theory. Lectures Given C.I.M.E. Summer School , vol.1932 , pp. 63-220


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.