메뉴 건너뛰기




Volumn 47, Issue 10, 2002, Pages 1590-1603

Stabilization of continuous-time jump linear systems

Author keywords

moment stabilizability; Almost sure stabilizability; Coupled Riccati equations; Jump linear systems

Indexed keywords

CONTINUOUS-TIME SYSTEMS;

EID: 0036804817     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2002.803528     Document Type: Article
Times cited : (178)

References (45)
  • 3
    • 0022518706 scopus 로고
    • Discrete-time Markovian-jump quadratic optimal control
    • H.J. Chizeck, A.S. Willsky, and D. Castanon, "Discrete-time Markovian-jump quadratic optimal control," Int. J. Control, vol. 43, no. 1, pp. 213-231, 1986.
    • (1986) Int. J. Control , vol.43 , Issue.1 , pp. 213-231
    • Chizeck, H.J.1    Willsky, A.S.2    Castanon, D.3
  • 4
    • 0011255931 scopus 로고
    • Limiting theorems for noncommutative operators
    • R. Bellman, "Limiting theorems for noncommutative operators," Duke Math. J., vol. 21, p. 456, 1960.
    • (1960) Duke Math. J. , vol.21 , pp. 456
    • Bellman, R.1
  • 5
    • 0011248763 scopus 로고
    • Stability of systems with randomly time-varying parameters
    • A.R. Bergen, "Stability of systems with randomly time-varying parameters," IRE Trans., vol. AC-5, p. 265, 1960.
    • (1960) IRE Trans. , vol.AC-5 , pp. 265
    • Bergen, A.R.1
  • 6
    • 0011230339 scopus 로고
    • Analysis of linear systems with randomly time-varying parameters
    • Brooklyn, NY: Poly. Inst.
    • A. Rosenbloom, "Analysis of linear systems with randomly time-varying parameters," in Proc. Symp. Inf. Nets. Brooklyn, NY: Poly. Inst., 1954, vol. III, p. 145.
    • (1954) Proc. Symp. Inf. Nets. , vol.2 , pp. 145
    • Rosenbloom, A.1
  • 8
    • 84904783359 scopus 로고
    • Statistical stability and output signal moments of a class of systems with random variation of structure
    • B.S. Darkhovskii and V.S. Leibovich, "Statistical stability and output signal moments of a class of systems with random variation of structure," Automat. Rem. Control, vol. 32, no. 10, pp. 1560-1567, 1971.
    • (1971) Automat. Rem. Control , vol.32 , Issue.10 , pp. 1560-1567
    • Darkhovskii, B.S.1    Leibovich, V.S.2
  • 9
    • 0007390824 scopus 로고
    • On the stability of systems with random parameters
    • I.I. Kats and N.N. Krasovskii, "On the stability of systems with random parameters," Prkil. Met. Mek., vol. 24, p. 809, 1960.
    • (1960) Prkil. Met. Mek. , vol.24 , pp. 809
    • Kats, I.I.1    Krasovskii, N.N.2
  • 10
    • 84936892579 scopus 로고
    • Stability of circuits with randomly time-varying parameters
    • Special Issue
    • J.E. Bertram and P.E. Sarachik, "Stability of circuits with randomly time-varying parameters," Trans. IRE, PGIT-5, Special Issue, p. 260, 1959.
    • (1959) Trans. IRE, PGIT-5 , pp. 260
    • Bertram, J.E.1    Sarachik, P.E.2
  • 11
    • 0026169870 scopus 로고
    • Stability and control of discrete-time jump linear systems
    • Y. Ji, H.J. Chizeck, X. Feng, and K.A. Loparo, "Stability and control of discrete-time jump linear systems," Control Theory Adv. Technol., vol. 7, no. 2, pp. 247-270, 1991.
    • (1991) Control Theory Adv. Technol. , vol.7 , Issue.2 , pp. 247-270
    • Ji, Y.1    Chizeck, H.J.2    Feng, X.3    Loparo, K.A.4
  • 12
    • 0025464943 scopus 로고
    • Controllability, stabilizability, and jump linear quadratic control
    • July
    • Y. Ji and H.J. Chizeck, "Controllability, stabilizability, and jump linear quadratic control," IEEE Trans. Automat. Contr., vol. 35, pp. 777-788, July 1990.
    • (1990) IEEE Trans. Automat. Contr. , vol.35 , pp. 777-788
    • Ji, Y.1    Chizeck, H.J.2
  • 13
    • 0014445822 scopus 로고
    • A survey of stability of stochastic systems
    • F. Kozin, "A survey of stability of stochastic systems," Automatica, vol. 5, pp. 95-112, 1969.
    • (1969) Automatica , vol.5 , pp. 95-112
    • Kozin, F.1
  • 14
    • 0002016710 scopus 로고
    • Lyapunov exponents
    • New York: Springer-Verlag
    • L. Arnold and V. Wihstutz, Lyapunov Exponents. New York: Springer-Verlag, 1985, Lecture Notes in Math., p. 1186.
    • (1985) Lecture Notes in Math. , pp. 1186
    • Arnold, L.1    Wihstutz, V.2
  • 15
    • 0001881373 scopus 로고
    • Almost sure and moment stability for linear Ito equations
    • Lyapunov Exponents: Proceeding, Bremen, L. Arnold and V. Whistutz, Eds. New York: Springer-Verlag
    • L. Arnold, E. Oelieklaus, and E. Pardoux, "Almost sure and moment stability for linear Ito equations," in Lyapunov Exponents: Proceeding, Bremen 1984, L. Arnold and V. Whistutz, Eds. New York: Springer-Verlag, 1986, Lecture Notes in Mathematics 1186.
    • (1984) Lecture Notes in Mathematics , vol.1186
    • Arnold, L.1    Oelieklaus, E.2    Pardoux, E.3
  • 16
    • 0001367492 scopus 로고
    • Stochastic stability analysis for continuous-time fault tolerant control systems
    • R. Srichander and B.R. Walker, "Stochastic stability analysis for continuous-time fault tolerant control systems," Int. J. Control, vol. 57, no. 2, pp. 433-452, 1993.
    • (1993) Int. J. Control , vol.57 , Issue.2 , pp. 433-452
    • Srichander, R.1    Walker, B.R.2
  • 17
    • 0020809682 scopus 로고
    • Multiplex control systems: Stochastic stability and reliability
    • G.S. Ladde and D.D. Šiljak, "Multiplex control systems: Stochastic stability and reliability," Int. J. Control, vol. 38, pp. 515-524, 1983.
    • (1983) Int. J. Control , vol.38 , pp. 515-524
    • Ladde, G.S.1    Šiljak, D.D.2
  • 18
  • 19
    • 0000465776 scopus 로고
    • Almost sure stability and δ-moment stability of jump linear systems
    • Y. Fang, K.A. Loparo, and X. Feng, "Almost sure stability and δ-moment stability of jump linear systems," Int. J. Control, vol. 59, no. 5, pp. 1281-1307, 1994.
    • (1994) Int. J. Control , vol.59 , Issue.5 , pp. 1281-1307
    • Fang, Y.1    Loparo, K.A.2    Feng, X.3
  • 20
    • 0001305048 scopus 로고
    • Stability of discrete time jump linear systems
    • _, "Stability of discrete time jump linear systems," J. Math. Syst., Estimat., Control, vol. 5, no. 3, pp. 275-321, 1995.
    • (1995) J. Math. Syst., Estimat., Control , vol.5 , Issue.3 , pp. 275-321
  • 22
    • 0024107920 scopus 로고
    • Almost sure and moment stability of jump linear systems
    • M. Mariton, "Almost sure and moment stability of jump linear systems," Syst. Control Lett., vol. 11, pp. 393-397, 1988.
    • (1988) Syst. Control Lett. , vol.11 , pp. 393-397
    • Mariton, M.1
  • 23
    • 0025449271 scopus 로고
    • Almost sure instability of the random harmonic oscillator
    • June
    • X. Feng and K.A. Loparo, "Almost sure instability of the random harmonic oscillator," SIAM J. Appl. Math., vol. 50, no. 3, pp. 744-759, June 1990.
    • (1990) SIAM J. Appl. Math. , vol.50 , Issue.3 , pp. 744-759
    • Feng, X.1    Loparo, K.A.2
  • 24
    • 0011245010 scopus 로고
    • On the Lyapunov exponent of a harmonic oscillator driven by a finite-state Markov processes
    • A. Leizarowitz, "On the Lyapunov exponent of a harmonic oscillator driven by a finite-state Markov processes," SIAM J. Appl. Math., vol. 49, no. 2, pp. 404-419, 1989.
    • (1989) SIAM J. Appl. Math. , vol.49 , Issue.2 , pp. 404-419
    • Leizarowitz, A.1
  • 25
    • 0001542758 scopus 로고
    • Estimates and exact expressions for Lyapunov exponents of stochastic linear differential equations
    • _, "Estimates and exact expressions for Lyapunov exponents of stochastic linear differential equations," Stochastics, vol. 24, pp. 335-356, 1988.
    • (1988) Stochastics , vol.24 , pp. 335-356
  • 26
    • 0025476464 scopus 로고
    • Exact results for the Lyapunov exponents of certain linear Ito systems
    • _, "Exact results for the Lyapunov exponents of certain linear Ito systems," SIAM J. Appl. Math., vol. 50, no. 4, pp. 1156-1165, 1990.
    • (1990) SIAM J. Appl. Math. , vol.50 , Issue.4 , pp. 1156-1165
  • 27
    • 0024132815 scopus 로고
    • Averaged dynamics and pole assignment for a class of stochastic systems
    • M. Mariton, "Averaged dynamics and pole assignment for a class of stochastic systems," Int. J. Control, vol. 48, no. 6, pp. 2169-2178, 1988.
    • (1988) Int. J. Control , vol.48 , Issue.6 , pp. 2169-2178
    • Mariton, M.1
  • 28
    • 0022135889 scopus 로고
    • A homotopy algorithm for solving coupled Riccati equations
    • M. Mariton and P. Bertrand, "A homotopy algorithm for solving coupled Riccati equations," Opt. Control Appl. Meth., vol. 6, pp. 351-357, 1985.
    • (1985) Opt. Control Appl. Meth. , vol.6 , pp. 351-357
    • Mariton, M.1    Bertrand, P.2
  • 30
    • 0024883224 scopus 로고
    • On largest Lyapunov exponent assignment and almost sure stabilization of hybrid systems
    • J. Ezzine and A.H. Haddad, "On largest Lyapunov exponent assignment and almost sure stabilization of hybrid systems," in Proc. Amer. Control Conf., 1989, pp. 805-810.
    • (1989) in Proc. Amer. Control Conf. , pp. 805-810
    • Ezzine, J.1    Haddad, A.H.2
  • 31
    • 0016567489 scopus 로고
    • On logarithmic norms
    • T. Ström, "On logarithmic norms," SIAM J. Numer. Anal., vol. 12, no. 5, pp. 741-753, 1975.
    • (1975) SIAM J. Numer. Anal. , vol.12 , Issue.5 , pp. 741-753
    • Ström, T.1
  • 37
    • 0002256901 scopus 로고
    • Random differential equations in control theory
    • A.T. Bharucha-Reid, Ed. New York: Academic
    • W.M. Wonham, "Random differential equations in control theory," in Probabilistic Methods in Applied Mathematics, A.T. Bharucha-Reid, Ed. New York: Academic, 1971, vol. 2.
    • (1971) Probabilistic Methods in Applied Mathematics , vol.2
    • Wonham, W.M.1
  • 38
    • 81255209428 scopus 로고    scopus 로고
    • A unified approach for mean square stability of continuous-time linear systems with Markovian jumping parameters and additive disturbances
    • M.D. Fragoso and O.L.V. Costa, "A unified approach for mean square stability of continuous-time linear systems with Markovian jumping parameters and additive disturbances,", LNCC Internal Rep. no. 11/99, 1999.
    • (1999) LNCC Internal Rep. , vol.11 , pp. 99
    • Fragoso, M.D.1    Costa, O.L.V.2
  • 39
    • 0034540437 scopus 로고    scopus 로고
    • Mean square stabilizability of continuous-time linear systems with partial information on the Markovian jumping parameters
    • June
    • _, "Mean square stabilizability of continuous-time linear systems with partial information on the Markovian jumping parameters," presented at the 2000 Amer Control Conf., June 2000.
    • (2000) 2000 Amer Control Conf.
  • 40
    • 21844522876 scopus 로고    scopus 로고
    • Stability and control for linear systems with jump Markov perturbations
    • T. Morozan, "Stability and control for linear systems with jump Markov perturbations," Stoch. Anal. Appl., vol. 13, pp. 1015-1022, 1996.
    • (1996) Stoch. Anal. Appl. , vol.13 , pp. 1015-1022
    • Morozan, T.1
  • 41
    • 0028494290 scopus 로고
    • Solution and asymptotic behavior of coupled Riccati equations in jump systems
    • Aug.
    • H. Abou-Kandil, G. Freiling, and G. Jank, "Solution and asymptotic behavior of coupled Riccati equations in jump systems," IEEE Trans. Automat. Contr., vol. 41, pp. 1631-1636, Aug. 1994.
    • (1994) IEEE Trans. Automat. Contr. , vol.41 , pp. 1631-1636
    • Abou-Kandil, H.1    Freiling, G.2    Jank, G.3
  • 42
    • 0033269095 scopus 로고    scopus 로고
    • Solutions for the linear quadratic control problem of Markov jump linear systems
    • J.B.R. do Val, J.C. Geromel, and O.L.V. Costa, "Solutions for the linear quadratic control problem of Markov jump linear systems," J. Optim. Theory Appl., vol. 203, pp. 283-311, 1999.
    • (1999) J. Optim. Theory Appl. , vol.203 , pp. 283-311
    • Do Val, J.B.R.1    Geromel, J.C.2    Costa, O.L.V.3
  • 43
    • 0033077957 scopus 로고    scopus 로고
    • 2-control of Markovian jump linear systems via convex analysis
    • 2-control of Markovian jump linear systems via convex analysis," Automatica, vol. 35, pp. 259-268, 1999.
    • (1999) Automatica , vol.35 , pp. 259-268
    • Costa, O.L.V.1    Do Vat, J.B.R.2    Geromel, J.C.3
  • 44
    • 0030287949 scopus 로고    scopus 로고
    • Robust state-feedback stabilization of jump linear systems
    • L. EIGhaou and M.A. Rami, "Robust state-feedback stabilization of jump linear systems," Int. J. Robust Nonlinear Control, vol. 6, pp. 1015-1022, 1996.
    • (1996) Int. J. Robust Nonlinear Control , vol.6 , pp. 1015-1022
    • EiGhaou, L.1    Rami, M.A.2
  • 45
    • 0030287555 scopus 로고    scopus 로고
    • LMI optimizations for nonstandard Riccati equations arising in stochastic control
    • Nov.
    • M.A. Rami and L. ElGhaoui, "LMI optimizations for nonstandard Riccati equations arising in stochastic control," IEEE Trans. Automat. Contr., vol. 41, pp. 1666-1671, Nov. 1996.
    • (1996) IEEE Trans. Automat. Contr. , vol.41 , pp. 1666-1671
    • Rami, M.A.1    ElGhaoui, L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.