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Volumn 46, Issue 6, 2010, Pages 1019-1027

Connection between cooperative positive systems and integral input-to-state stability of large-scale systems

Author keywords

Comparison system; Dissipation inequalities; Integral input to state stability (iISS); Lyapunov function; Monotone systems; Nonlinear gain; Nonlinear systems; Small gain condition

Indexed keywords

DISSIPATION INEQUALITIES; DISSIPATION INEQUALITY; INTEGRAL INPUT-TO-STATE STABILITY (IISS); MONOTONE SYSTEMS; NONLINEAR GAINS; SMALL-GAIN CONDITION;

EID: 77953130722     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2010.03.012     Document Type: Article
Times cited : (59)

References (32)
  • 2
    • 0034171635 scopus 로고    scopus 로고
    • Further equivalences and semiglobal versions of integral input to state stability
    • Angeli D., Sontag E.D., and Wang Y. Further equivalences and semiglobal versions of integral input to state stability. Dynamics and Control 10 2 (2000) 127-149
    • (2000) Dynamics and Control , vol.10 , Issue.2 , pp. 127-149
    • Angeli, D.1    Sontag, E.D.2    Wang, Y.3
  • 4
    • 0036928540 scopus 로고    scopus 로고
    • A unifying integral ISS framework for stability of nonlinear cascades
    • Arcak M., Angeli D., and Sontag E. A unifying integral ISS framework for stability of nonlinear cascades. SIAM Journal on Control and Optimization 40 6 (2002) 1888-1904
    • (2002) SIAM Journal on Control and Optimization , vol.40 , Issue.6 , pp. 1888-1904
    • Arcak, M.1    Angeli, D.2    Sontag, E.3
  • 7
    • 43549122575 scopus 로고    scopus 로고
    • Integral input to state stable systems in cascade
    • Chaillet A., and Angeli D. Integral input to state stable systems in cascade. Systems & Control Letters 57 7 (2008) 519-527
    • (2008) Systems & Control Letters , vol.57 , Issue.7 , pp. 519-527
    • Chaillet, A.1    Angeli, D.2
  • 8
    • 84955190508 scopus 로고    scopus 로고
    • On a small gain theorem for ISS networks in dissipative Lyapunov form
    • Budapest, Hungary pp
    • Dashkovskiy, S.N., Ito, H., & Wirth, F. R. (2009). On a small gain theorem for ISS networks in dissipative Lyapunov form. In Proc. European Contr. Conf., ECC2009. Budapest, Hungary (pp. 1077-1082).
    • (2009) Proc. European Contr. Conf., ECC2009 , pp. 1077-1082
    • Dashkovskiy, S.N.1    Ito, H.2    Wirth, F.R.3
  • 10
    • 77957358333 scopus 로고    scopus 로고
    • Dashkovskiy, S. N., Rüffer, B. S., & Wirth, F. R. (2009b). Small gain theorems for large scale systems and construction of ISS Lyapunov functions. In SIAM Journal on Control and Optimization (in press). Provisionally (accepted) September 3, 2009. http://arxiv.org/abs/0901.1842.
    • Dashkovskiy, S. N., Rüffer, B. S., & Wirth, F. R. (2009b). Small gain theorems for large scale systems and construction of ISS Lyapunov functions. In SIAM Journal on Control and Optimization (in press). Provisionally (accepted) September 3, 2009. http://arxiv.org/abs/0901.1842.
  • 11
    • 0003321315 scopus 로고    scopus 로고
    • Asymptotic behavior of dynamical and control systems under perturbation and discretization
    • Springer, Berlin
    • Grüne L. Asymptotic behavior of dynamical and control systems under perturbation and discretization. Lecture notes in mathematics Vol. 1783 (2002), Springer, Berlin
    • (2002) Lecture notes in mathematics , vol.1783
    • Grüne, L.1
  • 12
    • 0036742738 scopus 로고    scopus 로고
    • Input-to-state dynamical stability and its Lyapunov function characterization
    • Grüne L. Input-to-state dynamical stability and its Lyapunov function characterization. IEEE Transactions on Automatic Control 47 9 (2002) 1499-1504
    • (2002) IEEE Transactions on Automatic Control , vol.47 , Issue.9 , pp. 1499-1504
    • Grüne, L.1
  • 15
    • 33750125424 scopus 로고    scopus 로고
    • State-dependent scaling problems and stability of interconnected iISS and ISS systems
    • Ito H. State-dependent scaling problems and stability of interconnected iISS and ISS systems. IEEE Transactions on Automatic Control 51 10 (2006) 1626-1643
    • (2006) IEEE Transactions on Automatic Control , vol.51 , Issue.10 , pp. 1626-1643
    • Ito, H.1
  • 16
    • 85128566305 scopus 로고    scopus 로고
    • Ito, H. (2008). A Lyapunov approach to integral input-to-state stability of cascaded systems with external signals. In Proc. 47th IEEE conf. decis. control. Cancun, Mexico (pp. 628-633), December 9-11, 2008.
    • Ito, H. (2008). A Lyapunov approach to integral input-to-state stability of cascaded systems with external signals. In Proc. 47th IEEE conf. decis. control. Cancun, Mexico (pp. 628-633), December 9-11, 2008.
  • 17
    • 0000574179 scopus 로고
    • Ein Beweis des Fixpunktsatzes für n-dimensionale Simplexe
    • Knaster B., Kuratowski C., and Mazurkiewicz S. Ein Beweis des Fixpunktsatzes für n-dimensionale Simplexe. Fundamenta 14 (1929) 132-137
    • (1929) Fundamenta , vol.14 , pp. 132-137
    • Knaster, B.1    Kuratowski, C.2    Mazurkiewicz, S.3
  • 20
    • 33750835760 scopus 로고
    • Vector Lyapunov functions and stability analysis of nonlinear systems
    • Kluwer Academic Publishers Group, Dordrecht
    • Lakshmikantham V., Matrosov V.M., and Sivasundaram S. Vector Lyapunov functions and stability analysis of nonlinear systems. Mathematics and its applications Vol. 63 (1991), Kluwer Academic Publishers Group, Dordrecht
    • (1991) Mathematics and its applications , vol.63
    • Lakshmikantham, V.1    Matrosov, V.M.2    Sivasundaram, S.3
  • 24
    • 77953476491 scopus 로고    scopus 로고
    • Monotone inequalities, dynamical systems, and paths in the positive orthant of Euclidean n-space
    • in press doi:10.1007/s11117-009-0016-5
    • Rüffer, B.S. (2009). Monotone inequalities, dynamical systems, and paths in the positive orthant of Euclidean n-space. Positivity. in press (doi:10.1007/s11117-009-0016-5).
    • (2009) Positivity
    • Rüffer, B.S.1
  • 25
    • 0003270907 scopus 로고
    • Monotone dynamical systems
    • American Mathematical Society, Providence, RI
    • Smith H.L. Monotone dynamical systems. Mathematical surveys and monographs Vol. 41 (1995), American Mathematical Society, Providence, RI
    • (1995) Mathematical surveys and monographs , vol.41
    • Smith, H.L.1
  • 26
    • 0348241184 scopus 로고    scopus 로고
    • Comments on integral variants of ISS
    • Sontag E.D. Comments on integral variants of ISS. Systems & Control Letters 34 1-2 (1998) 93-100
    • (1998) Systems & Control Letters , vol.34 , Issue.1-2 , pp. 93-100
    • Sontag, E.D.1
  • 27
    • 0000454435 scopus 로고    scopus 로고
    • The ISS philosophy as a unifying framework for stability-like behavior
    • Nonlinear control in the year 2000, vol. 2 (Paris), Springer, London
    • Sontag E.D. The ISS philosophy as a unifying framework for stability-like behavior. Nonlinear control in the year 2000, vol. 2 (Paris). Lecture notes in control and inform. sci. Vol. 259 (2001), Springer, London 443-467
    • (2001) Lecture notes in control and inform. sci. , vol.259 , pp. 443-467
    • Sontag, E.D.1
  • 28
    • 0037534020 scopus 로고    scopus 로고
    • An example of a GAS system which can be destabilized by an integrable perturbation
    • Sontag E.D., and Krichman M. An example of a GAS system which can be destabilized by an integrable perturbation. IEEE Transactions on Automatic Control 48 6 (2003) 1046-1049
    • (2003) IEEE Transactions on Automatic Control , vol.48 , Issue.6 , pp. 1046-1049
    • Sontag, E.D.1    Krichman, M.2
  • 29
    • 0029358183 scopus 로고
    • Changing supply functions in input/state stable systems
    • Sontag E.D., and Teel A. Changing supply functions in input/state stable systems. IEEE Transactions on Automatic Control 40 8 (1995) 1476-1478
    • (1995) IEEE Transactions on Automatic Control , vol.40 , Issue.8 , pp. 1476-1478
    • Sontag, E.D.1    Teel, A.2
  • 30
    • 0029288045 scopus 로고
    • On characterizations of the input-to-state stability property
    • Sontag E.D., and Wang Y. On characterizations of the input-to-state stability property. Systems & Control Letters 24 5 (1995) 351-359
    • (1995) Systems & Control Letters , vol.24 , Issue.5 , pp. 351-359
    • Sontag, E.D.1    Wang, Y.2
  • 31
    • 0030244538 scopus 로고    scopus 로고
    • New characterizations of input-to-state stability
    • Sontag E.D., and Wang Y. New characterizations of input-to-state stability. IEEE Transactions on Automatic Control 41 9 (1996) 1283-1294
    • (1996) IEEE Transactions on Automatic Control , vol.41 , Issue.9 , pp. 1283-1294
    • Sontag, E.D.1    Wang, Y.2
  • 32
    • 0034426073 scopus 로고    scopus 로고
    • A smooth Lyapunov function from a class-K L estimate involving two positive semidefinite functions
    • Teel A.R., and Praly L. A smooth Lyapunov function from a class-K L estimate involving two positive semidefinite functions. ESAIM: Control, Optimisation and Calculus of Variations 5 (2000) 313-367
    • (2000) ESAIM: Control, Optimisation and Calculus of Variations , vol.5 , pp. 313-367
    • Teel, A.R.1    Praly, L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.