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Volumn 20, Issue 1, 2003, Pages 89-103

Linear approximations to nonlinear dynamical systems with applications to stability and spectral theory

Author keywords

Linear approximations; Nonlinear systems; Spectral theory; Stability

Indexed keywords

APPROXIMATION THEORY; ASYMPTOTIC STABILITY; CONTROL SYSTEM ANALYSIS; FREQUENCY DOMAIN ANALYSIS; LINEAR SYSTEMS; LINEARIZATION; SPECTRUM ANALYSIS; TIME VARYING CONTROL SYSTEMS;

EID: 0037335382     PISSN: 02650754     EISSN: None     Source Type: Journal    
DOI: 10.1093/imamci/20.1.89     Document Type: Article
Times cited : (49)

References (15)
  • 2
    • 0036351258 scopus 로고    scopus 로고
    • Lagrangian manifolds, viscosity solutions and Maslov index
    • McCaffrey, D. & Banks, S. P. (2002) Lagrangian manifolds, viscosity solutions and Maslov index. J. Convex Analysis, 9, 185-224.
    • (2002) J. Convex Analysis , vol.9 , pp. 185-224
    • McCaffrey, D.1    Banks, S.P.2
  • 3
    • 0012347013 scopus 로고
    • Nonlinear systems, the Lie series and the left shift operator: Application to nonlinear optimal control
    • Banks, S. P. & Iddir, N. (1992) Nonlinear systems, the Lie series and the left shift operator: application to nonlinear optimal control. IMA J. Math. Contr. Inf., 9, 23-34.
    • (1992) IMA J. Math. Contr. Inf. , vol.9 , pp. 23-34
    • Banks, S.P.1    Iddir, N.2
  • 4
    • 0012292899 scopus 로고
    • Infinite-dimensional Carleman linearisation, the Lie series and optimal control of nonlinear PDEs
    • Banks, S. P. (1992) Infinite-dimensional Carleman linearisation, the Lie series and optimal control of nonlinear PDEs. Int J. Sys. Sci., 23, 663-675.
    • (1992) Int J. Sys. Sci. , vol.23 , pp. 663-675
    • Banks, S.P.1
  • 6
    • 0012347014 scopus 로고    scopus 로고
    • The Schwartz' kernel theorem and the frequency-domain theory of nonlinear systems
    • Banks, S. P., Riddalls, C. & McCaffrey, D, (1997) 'The Schwartz' kernel theorem and the frequency-domain theory of nonlinear systems. Arch. Cont. Sci., 6 (XLII), 57-73.
    • (1997) Arch. Cont. Sci. , vol.6 , Issue.42 , pp. 57-73
    • Banks, S.P.1    Riddalls, C.2    McCaffrey, D.3
  • 8
    • 0034562543 scopus 로고    scopus 로고
    • Approximate optimal control and stability of nonlinear finite and infinite-dimensional systems
    • Banks, S. P. & Dinesh, K. (2000) Approximate optimal control and stability of nonlinear finite and infinite-dimensional systems. Ann. Op. Res., 98, 19-44.
    • (2000) Ann. Op. Res. , vol.98 , pp. 19-44
    • Banks, S.P.1    Dinesh, K.2
  • 9
    • 0036248046 scopus 로고    scopus 로고
    • Nonlinear delay systems, Lie algebras and Lyapunov transformations
    • Banks, S. P. (2002) Nonlinear delay systems, Lie algebras and Lyapunov transformations. IMA J. Math. Cont. Inf., 19, 59-72.
    • (2002) IMA J. Math. Cont. Inf. , vol.19 , pp. 59-72
    • Banks, S.P.1
  • 10
    • 0040689421 scopus 로고    scopus 로고
    • Lie algebras, structure of nonlinear systems and chaotic motion
    • Banks, S. P. & McCaffrey, D, (1998) Lie algebras, structure of nonlinear systems and chaotic motion. Int. J. Bifurcation & Chaos, 8, 1437-1462.
    • (1998) Int. J. Bifurcation & Chaos , vol.8 , pp. 1437-1462
    • Banks, S.P.1    McCaffrey, D.2
  • 11
    • 0035262750 scopus 로고    scopus 로고
    • The Lie algebra of a dynamical system and its application to control
    • Banks, S. P. (2001) The Lie algebra of a dynamical system and its application to control. Int. J. Sys. Sci., 32, 220-238.
    • (2001) Int. J. Sys. Sci. , vol.32 , pp. 220-238
    • Banks, S.P.1
  • 13
    • 84984131619 scopus 로고
    • Control system analysis and design via the second method of Lyapunov
    • Kalman, R.E. & Bertram, (1960) Control system analysis and design via the second method of Lyapunov, ASME J. Basic Eng., 82, 371-393.
    • (1960) ASME J. Basic Eng. , vol.82 , pp. 371-393
    • Kalman, R.E.1    Bertram2
  • 15
    • 49349126301 scopus 로고
    • A spectral theory for linear differential systems
    • Sacker, R. J. & Sell, G. (1978) A spectral theory for linear differential systems. J. Diff. Eqn., 27, 320-358.
    • (1978) J. Diff. Eqn. , vol.27 , pp. 320-358
    • Sacker, R.J.1    Sell, G.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.