메뉴 건너뛰기




Volumn 38, Issue 4, 2000, Pages 1241-1264

Parameterized LMIs in control theory

Author keywords

[No Author keywords available]

Indexed keywords

LYAPUNOV METHODS; PARAMETER ESTIMATION; QUADRATIC PROGRAMMING; ROBUSTNESS (CONTROL SYSTEMS); SYSTEM STABILITY;

EID: 0033682337     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S036301299732612X     Document Type: Article
Times cited : (220)

References (47)
  • 1
    • 0031673619 scopus 로고    scopus 로고
    • Advanced gain-scheduling techniques for uncertain systems
    • P. APKARIAN AND R. J. ADAMS, Advanced gain-scheduling techniques for uncertain systems, IEEE Trans. Control System Tech., 6 (1997), pp. 21-32.
    • (1997) IEEE Trans. Control System Tech. , vol.6 , pp. 21-32
    • Apkarian, P.1    Adams, R.J.2
  • 4
    • 0032207223 scopus 로고    scopus 로고
    • Robust convex optimization
    • A. BEN-TAL AND A. NEMIROVSKI, Robust convex optimization, Math. Oper. Res., 23 (1998), pp. 769-805.
    • (1998) Math. Oper. Res. , vol.23 , pp. 769-805
    • Ben-Tal, A.1    Nemirovski, A.2
  • 5
    • 0032664938 scopus 로고    scopus 로고
    • Robust solutions to uncertain linear problems
    • A. BEN-TAL AND A. NEMIROVSKI, Robust solutions to uncertain linear problems, Oper. Res. Lett., 25 (1999), pp. 1-13.
    • (1999) Oper. Res. Lett. , vol.25 , pp. 1-13
    • Ben-Tal, A.1    Nemirovski, A.2
  • 6
    • 0031285674 scopus 로고    scopus 로고
    • Robust truss topology design via semidefinite programming
    • A. BEN-TAL AND A. NEMIROVSKI, Robust Truss topology design via semidefinite programming, SIAM J. Optim., 7 (1997), pp. 991-1016.
    • (1997) SIAM J. Optim. , vol.7 , pp. 991-1016
    • Ben-Tal, A.1    Nemirovski, A.2
  • 7
    • 0024699749 scopus 로고
    • A linear programming oriented procedure for quadratic stabilization of uncertain systems
    • J. BERNUSSOU, P. L. D. PERES, AND J. C. GEROMEL, A linear programming oriented procedure for quadratic stabilization of uncertain systems, Systems Control Lett., 13 (1989), pp. 65-72.
    • (1989) Systems Control Lett. , vol.13 , pp. 65-72
    • Bernussou, J.1    Peres, P.L.D.2    Geromel, J.C.3
  • 8
    • 43949163936 scopus 로고
    • Method of centers for minimizing generalized eigenvalues
    • S. BOYD AND L. ELGHAOUI, Method of centers for minimizing generalized eigenvalues, Linear Algebra Appl., 188 (1992), pp. 63-111.
    • (1992) Linear Algebra Appl. , vol.188 , pp. 63-111
    • Boyd, S.1    ElGhaoui, L.2
  • 9
    • 0003004622 scopus 로고
    • Linear matrix inequalities in systems and control theory
    • SIAM, Philadelphia
    • S. BOYD, L. ELGHAOUI, E. FERON, AND V. BALAKRISHNAN, Linear Matrix Inequalities in Systems and Control Theory, SIAM Stud. Appl. Math., 15, SIAM, Philadelphia, 1994.
    • (1994) SIAM Stud. Appl. Math. , vol.15
    • Boyd, S.1    ElGhaoui, L.2    Feron, E.3    Balakrishnan, V.4
  • 11
    • 0020203138 scopus 로고
    • Analysis of feedback systems with structured uncertainties
    • J. DOYLE, Analysis of feedback systems with structured uncertainties, Proc. IEE-D, 129 (1982), pp. 242-250.
    • (1982) Proc. IEE-D , vol.129 , pp. 242-250
    • Doyle, J.1
  • 13
    • 0025747144 scopus 로고
    • Robustness in the presence of mixed parametric uncertainty and unmodeled dynamics
    • M. K. H. FAN, A. L. TITS, AND J. C. DOYLE, Robustness in the presence of mixed parametric uncertainty and unmodeled dynamics, IEEE Trans. Automat. Control, AC-36 (1991), pp. 25-38.
    • (1991) IEEE Trans. Automat. Control , vol.AC-36 , pp. 25-38
    • Fan, M.K.H.1    Tits, A.L.2    Doyle, J.C.3
  • 14
    • 0013292935 scopus 로고
    • The S-procedure and duality relations in nonconvex problems of quadratic programming
    • In Russian, 1973
    • A. L. FRADKOV AND V. A. YAKUBOVICH, The S-procedure and duality relations in nonconvex problems of quadratic programming, Vestn. Lening. Univ. Math., 6 (1979), pp. 101-109. In Russian, 1973.
    • (1979) Vestn. Lening. Univ. Math. , vol.6 , pp. 101-109
    • Fradkov, A.L.1    Yakubovich, V.A.2
  • 15
    • 0031259375 scopus 로고    scopus 로고
    • Improved upper bounds for the mixed structured singular value
    • M. FU AND N. E. BARABANOV, Improved upper bounds for the mixed structured singular value, IEEE Trans. Automat. Control, 42 (1997), pp. 1447-1452.
    • (1997) IEEE Trans. Automat. Control , vol.42 , pp. 1447-1452
    • Fu, M.1    Barabanov, N.E.2
  • 18
    • 0030106702 scopus 로고    scopus 로고
    • Parameter-dependent Lyapunov functions for real parametric uncertainty
    • P. GAHINET, P. APKARIAN, AND M. CHILALI, Parameter-dependent Lyapunov functions for real parametric uncertainty, IEEE Trans. Automat. Control, 41 (1996), pp. 436-442.
    • (1996) IEEE Trans. Automat. Control , vol.41 , pp. 436-442
    • Gahinet, P.1    Apkarian, P.2    Chilali, M.3
  • 22
    • 0028484180 scopus 로고
    • ∞ control problem: LMI existence conditions and state space formulas
    • ∞ control problem: LMI existence conditions and state space formulas, Automatica J. IFAC, 30 (1994), pp. 1307-1317.
    • (1994) Automatica J. IFAC , vol.30 , pp. 1307-1317
    • Iwasaki, T.1    Skelton, R.E.2
  • 23
    • 0027656654 scopus 로고
    • An interior-point method for minimizing the maximum eigenvalue of a linear combination of matrices
    • F. JARRE, An interior-point method for minimizing the maximum eigenvalue of a linear combination of matrices, SIAM J. Control Optim., 31 (1993), pp. 1360-1377.
    • (1993) SIAM J. Control Optim. , vol.31 , pp. 1360-1377
    • Jarre, F.1
  • 25
    • 0029377475 scopus 로고
    • ∞ control of nonlinear systems: A convex characterization
    • ∞ Control of nonlinear systems: A convex characterization, IEEE Trans. Automat. Control, 40 (1995), pp. 1668-1674.
    • (1995) IEEE Trans. Automat. Control , vol.40 , pp. 1668-1674
    • Lu, W.1    Doyle, J.C.2
  • 27
    • 0031144412 scopus 로고    scopus 로고
    • The projective method for solving linear matrix inequalities
    • A. NEMIROVSKI AND P. GAHINET, The projective method for solving linear matrix inequalities, Math. Programming, 77 (1997), pp. 163-190.
    • (1997) Math. Programming , vol.77 , pp. 163-190
    • Nemirovski, A.1    Gahinet, P.2
  • 28
    • 0041621392 scopus 로고    scopus 로고
    • Interior point polynomial methods in convex programming: Theory and applications
    • SIAM, Philadelphia
    • Y. E. NESTEROV AND A. S. NEMIROVSKI, Interior Point Polynomial Methods in Convex Programming: Theory and Applications, SIAM Stud. Appl. Math. 13, SIAM, Philadelphia, 1994.
    • SIAM Stud. Appl. Math. , vol.13 , pp. 1994
    • Nesterov, Y.E.1    Nemirovski, A.S.2
  • 29
    • 0032252302 scopus 로고    scopus 로고
    • Robust solutions to uncertain semidefinite programs
    • F. OUSTRY, L. ELGHAOUI, AND H. LEBRET, Robust solutions to uncertain semidefinite programs, SIAM J. Optim., 9 (1998), pp. 33-52.
    • (1998) SIAM J. Optim. , vol.9 , pp. 33-52
    • Oustry, F.1    Elghaoui, L.2    Lebret, H.3
  • 30
    • 0028379059 scopus 로고
    • Gain scheduling via linear fractional transformations
    • A. PACKARD, Gain scheduling via linear fractional transformations, Systems Control Lett., 22 (1994), pp. 79-92.
    • (1994) Systems Control Lett. , vol.22 , pp. 79-92
    • Packard, A.1
  • 31
    • 0022757589 scopus 로고
    • A Riccati equation approach to the stabilization of uncertain linear systems
    • I. R. PETERSEN AND C. V. HOLLOT, A Riccati equation approach to the stabilization of uncertain linear systems, Automatica J. IFAC, 22 (1986), pp. 397-411.
    • (1986) Automatica J. IFAC , vol.22 , pp. 397-411
    • Petersen, I.R.1    Hollot, C.V.2
  • 32
    • 0027307460 scopus 로고
    • Checking robust nonsingularity is NP-complete
    • S. POLJAK AND J. ROHN, Checking robust nonsingularity is NP-complete, Math. Control Signals Systems, 6 (1994), pp. 1-9.
    • (1994) Math. Control Signals Systems , vol.6 , pp. 1-9
    • Poljak, S.1    Rohn, J.2
  • 33
    • 0025551469 scopus 로고
    • Robust autopilot design using μ-synthesis
    • San Diego, CA, IFAC
    • R. T. REICHERT, Robust autopilot design using μ-synthesis, in Proceedings of the American Control Conference, San Diego, CA, IFAC, 1990, pp. 2368-2373.
    • (1990) Proceedings of the American Control Conference , pp. 2368-2373
    • Reichert, R.T.1
  • 36
    • 0021562105 scopus 로고
    • Minimizing conservativeness of robust singular values
    • S. G. Tzafestas, ed., Reidel, Dordrecht, Boston, London
    • M. G. SAFONOV AND J. DOYLE, Minimizing conservativeness of robust singular values, in Multivariable Control, S. G. Tzafestas, ed., Reidel, Dordrecht, Boston, London, 1984, pp. 197-207.
    • (1984) Multivariable Control , pp. 197-207
    • Safonov, M.G.1    Doyle, J.2
  • 39
    • 0024702003 scopus 로고
    • Parameter space methods for robust control design: A guided tour
    • D. D. SILJAK, Parameter space methods for robust control design: A guided tour, IEEE Trans. Automat. Control, 34 (1989), pp. 674-688.
    • (1989) IEEE Trans. Automat. Control , vol.34 , pp. 674-688
    • Siljak, D.D.1
  • 40
    • 0033077650 scopus 로고    scopus 로고
    • Relaxations of parameterized LMIs with control applications
    • H. D. TUAN AND P. APKARIAN, Relaxations of parameterized LMIs with control applications, Internat. J. Robust Nonlinear Control, 9 (1999), pp. 59-84.
    • (1999) Internat. J. Robust Nonlinear Control , vol.9 , pp. 59-84
    • Tuan, H.D.1    Apkarian, P.2
  • 42
    • 0029338589 scopus 로고
    • Primal-dual potential reduction method for problems involving matrix inequalities
    • L. VANDENBERGHE AND S. BOYD, Primal-dual potential reduction method for problems involving matrix inequalities, Math. Programming Ser. B, 69 (1995), pp. 205-236.
    • (1995) Math. Programming Ser. B , vol.69 , pp. 205-236
    • Vandenberghe, L.1    Boyd, S.2
  • 43
    • 0030106462 scopus 로고    scopus 로고
    • Semidefinite programming
    • L. VANDENBERGHE AND S. BOYD, Semidefinite programming, SIAM Rev., 38 (1996), pp. 49-95.
    • (1996) SIAM Rev. , vol.38 , pp. 49-95
    • Vandenberghe, L.1    Boyd, S.2
  • 45
    • 0002182462 scopus 로고
    • The S-procedure in non-linear control theory
    • In Russian, 1971
    • V. A. YAKUBOVICH, The S-procedure in non-linear control theory, Vestnik Leningrad Univ. Math., 4 (1977), pp. 73-93. In Russian, 1971.
    • (1977) Vestnik Leningrad Univ. Math. , vol.4 , pp. 73-93
    • Yakubovich, V.A.1
  • 47
    • 0000451507 scopus 로고    scopus 로고
    • ∞ control with parametric Lyapunov functions
    • ∞ control with parametric Lyapunov functions, Systems Control Lett., 30 (1997), pp. 57-69.
    • (1997) Systems Control Lett. , vol.30 , pp. 57-69
    • Yu, J.1    Sideris, A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.