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Volumn 51, Issue 11, 2006, Pages 1770-1786

Stability and performance for saturated systems via quadratic and nonquadratic Lyapunov functions

Author keywords

Deadzone; Domain of attraction; Lyapunov functions; Nonlinear L2; Reachable set; Saturation

Indexed keywords

FEEDBACK CONTROL; LYAPUNOV METHODS; MATRIX ALGEBRA;

EID: 33846783825     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2006.884942     Document Type: Article
Times cited : (243)

References (55)
  • 1
    • 0029266878 scopus 로고
    • "Nonquadratic Lyapunov functions for robust control"
    • F. Blanchini, "Nonquadratic Lyapunov functions for robust control," Automatica, vol. 31, pp. 451-461, 1995.
    • (1995) Automatica , vol.31 , pp. 451-461
    • Blanchini, F.1
  • 3
    • 0018453090 scopus 로고
    • "Stability of dynamical systems: A constructive approach"
    • Apr
    • R. K. Brayton and C. H. Tong, "Stability of dynamical systems: A constructive approach," IEEE Trans. Circuits Syst., vol. CAS-26, no. 4, pp. 224-234, Apr. 1979.
    • (1979) IEEE Trans. Circuits Syst. , vol.CAS-26 , Issue.4 , pp. 224-234
    • Brayton, R.K.1    Tong, C.H.2
  • 4
    • 2442583020 scopus 로고    scopus 로고
    • "Anti-windup design of output tracking systems subject to actuator saturation and constant disturbances"
    • Y. Y. Cao, Z. Lin, and D. G. Ward, "Anti-windup design of output tracking systems subject to actuator saturation and constant disturbances," Automatica, vol. 40, no. 7, pp. 1221-1228, 2004.
    • (2004) Automatica , vol.40 , Issue.7 , pp. 1221-1228
    • Cao, Y.Y.1    Lin, Z.2    Ward, D.G.3
  • 5
    • 0036256863 scopus 로고    scopus 로고
    • "An antiwindup approach to enlarging domain of attraction for linear systems subject to actuator saturation"
    • Jan
    • Y. Y. Cao, Z. Lin, and D. G. Ward, "An antiwindup approach to enlarging domain of attraction for linear systems subject to actuator saturation," IEEE Trans. Autom. Control, vol. 47, no. 1, pp. 140-145, Jan. 2002.
    • (2002) IEEE Trans. Autom. Control , vol.47 , Issue.1 , pp. 140-145
    • Cao, Y.Y.1    Lin, Z.2    Ward, D.G.3
  • 7
    • 0038372478 scopus 로고    scopus 로고
    • "Homogeneous Lyapunov functions for systems with structured uncertainties"
    • G. Chesi, A. Garulli, A. Tesi, and A. Vicino, "Homogeneous Lyapunov functions for systems with structured uncertainties," Automatica, vol. 39, pp. 1027-1035, 2003.
    • (2003) Automatica , vol.39 , pp. 1027-1035
    • Chesi, G.1    Garulli, A.2    Tesi, A.3    Vicino, A.4
  • 8
    • 0036055664 scopus 로고    scopus 로고
    • "Anti-windup for local stability of unstable plants"
    • in Anchorage, AK, May
    • S. Crawshaw and G. Vinnicombe, "Anti-windup for local stability of unstable plants," in Proc. Amer. Control Conf., Anchorage, AK, May 2002, pp. 645-650.
    • (2002) Proc. Amer. Control Conf. , pp. 645-650
    • Crawshaw, S.1    Vinnicombe, G.2
  • 10
    • 12944254315 scopus 로고    scopus 로고
    • "Anti-windup design with guaranteed regions of stability: An LMI-based approach"
    • Jan
    • J. M. G. da Silva, Jr and S. Tarbouriech, "Anti-windup design with guaranteed regions of stability: An LMI-based approach," IEEE Trans. Autom. Control, vol. 50, no. 1, pp. 106-111, Jan. 2005.
    • (2005) IEEE Trans. Autom. Control , vol.50 , Issue.1 , pp. 106-111
    • da Silva Jr., J.M.G.1    Tarbouriech, S.2
  • 11
    • 0032625112 scopus 로고    scopus 로고
    • "A converse Lyapunov theorem for a class of dynamical systems which undergo switching"
    • Apr
    • W. P. Dayawansa and C. F. Martin, "A converse Lyapunov theorem for a class of dynamical systems which undergo switching," IEEE Trans. Autom. Control, vol. 44, no. 4, pp. 751-760, Apr. 1999.
    • (1999) IEEE Trans. Autom. Control , vol.44 , Issue.4 , pp. 751-760
    • Dayawansa, W.P.1    Martin, C.F.2
  • 12
    • 0033116223 scopus 로고    scopus 로고
    • "An anti-windup scheme with closed-loop stability considerations"
    • C. Edwards and I. Postlethwaite, "An anti-windup scheme with closed-loop stability considerations," Automatica, vol. 35, no. 4, pp. 761-765, 1999.
    • (1999) Automatica , vol.35 , Issue.4 , pp. 761-765
    • Edwards, C.1    Postlethwaite, I.2
  • 13
    • 2442442814 scopus 로고    scopus 로고
    • 2 -disturbances"
    • 2 -disturbances," Automatica, vol. 40, no. 7, pp. 1229-1238, 2004.
    • (2004) Automatica , vol.40 , Issue.7 , pp. 1229-1238
    • Fang, H.1    Lin, Z.2    Hu, T.3
  • 14
    • 84992511611 scopus 로고    scopus 로고
    • "Dual matrix inequalities in stability and performance analysis of linear differential/difference inclusions"
    • in Norwell, MA: Birkhäuser
    • R. Goebel, T. Hu, and A. R. Teel, "Dual matrix inequalities in stability and performance analysis of linear differential/difference inclusions," in Current Trends in Nonlinear Systems and Control. Norwell, MA: Birkhäuser, 2005, pp. 103-122.
    • (2005) Current Trends in Nonlinear Systems and Control , pp. 103-122
    • Goebel, R.1    Hu, T.2    Teel, A.R.3
  • 15
    • 14244260544 scopus 로고    scopus 로고
    • "Dissipativity for dual linear differential inclusions through conjugate storage functions"
    • R. Goebel, A. R. Teel, T. Hu, and Z. Lin, "Dissipativity for dual linear differential inclusions through conjugate storage functions," in Proc. IEEE Conf. Decision and Control, 2004, pp. 2700-2705.
    • (2004) Proc. IEEE Conf. Decision and Control , pp. 2700-2705
    • Goebel, R.1    Teel, A.R.2    Hu, T.3    Lin, Z.4
  • 17
    • 4344713236 scopus 로고    scopus 로고
    • "Robust linear anti-windup synthesis for recovery of unconstrained performance"
    • G. Grimm, A. R. Teel, and L. Zaccarian, "Robust linear anti-windup synthesis for recovery of unconstrained performance," Int. J. Robust Nonlinear Control, vol. 14, no. 13-15, pp. 1133-1168, 2004.
    • (2004) Int. J. Robust Nonlinear Control , vol.14 , Issue.13-15 , pp. 1133-1168
    • Grimm, G.1    Teel, A.R.2    Zaccarian, L.3
  • 18
    • 4444305401 scopus 로고    scopus 로고
    • "Linear LMI-based external anti-windup augmentation for stable linear systems"
    • G. Grimm, A. R. Teel, and L. Zaccarian, "Linear LMI-based external anti-windup augmentation for stable linear systems," Automatica, vol. 40, no. 11, pp. 1987-1996, 2004.
    • (2004) Automatica , vol.40 , Issue.11 , pp. 1987-1996
    • Grimm, G.1    Teel, A.R.2    Zaccarian, L.3
  • 19
    • 0028447982 scopus 로고
    • "H∞ control of systems under norm bounded uncertainties in all system matrices"
    • Jun
    • K. Gu, "H∞ control of systems under norm bounded uncertainties in all system matrices," IEEE Trans. Autom. Control, vol. 39, no. 6, pp. 1320-1322, Jun. 1994.
    • (1994) IEEE Trans. Autom. Control , vol.39 , Issue.6 , pp. 1320-1322
    • Gu, K.1
  • 20
    • 0033283467 scopus 로고    scopus 로고
    • "A path-following method for solving BMI problems in control"
    • A. Hassibi, J. How, and S. Boyd, "A path-following method for solving BMI problems in control," in Proc. Amer. Control Conf., 1999, pp. 1385-1389.
    • (1999) Proc. Amer. Control Conf. , pp. 1385-1389
    • Hassibi, A.1    How, J.2    Boyd, S.3
  • 21
    • 0032280895 scopus 로고    scopus 로고
    • "Analysis of linear systems with saturation using convex optimization"
    • H. Hindi and S. Boyd, "Analysis of linear systems with saturation using convex optimization," in Proc. 37th Conf. Decision Control, 1998, pp. 903-908.
    • (1998) Proc. 37th Conf. Decision Control , pp. 903-908
    • Hindi, H.1    Boyd, S.2
  • 23
    • 0037349314 scopus 로고    scopus 로고
    • "Composite quadratic Lyapunov functions for constrained control systems"
    • Mar
    • T. Hu and Z. Lin, "Composite quadratic Lyapunov functions for constrained control systems," IEEE Trans. Autom. Control, vol. 48, no. 3, pp. 440-450, Mar. 2003.
    • (2003) IEEE Trans. Autom. Control , vol.48 , Issue.3 , pp. 440-450
    • Hu, T.1    Lin, Z.2
  • 24
    • 3843073156 scopus 로고    scopus 로고
    • "Properties of convex hull quadratic Lyapunov functions"
    • Jul
    • T. Hu and Z. Lin, "Properties of convex hull quadratic Lyapunov functions," IEEE Trans. Autom. Control, vol. 49, no. 7, pp. 1162-1167, Jul. 2004.
    • (2004) IEEE Trans. Autom. Control , vol.49 , Issue.7 , pp. 1162-1167
    • Hu, T.1    Lin, Z.2
  • 25
    • 0036466753 scopus 로고    scopus 로고
    • "An analysis and design method for linear systems subject to actuator saturation and disturbance"
    • T. Hu, Z. Lin, and B. M. Chen, "An analysis and design method for linear systems subject to actuator saturation and disturbance," Automatica, vol. 38, no. 2, pp. 351-359, 2002.
    • (2002) Automatica , vol.38 , Issue.2 , pp. 351-359
    • Hu, T.1    Lin, Z.2    Chen, B.M.3
  • 26
    • 0037082850 scopus 로고    scopus 로고
    • "Analysis and design for linear discrete-time systems subject to actuator saturation"
    • T. Hu, Z. Lin, and B. M. Chen, "Analysis and design for linear discrete-time systems subject to actuator saturation," Syst. Control Lett., vol. 45, no. 2, pp. 97-112, 2002.
    • (2002) Syst. Control Lett. , vol.45 , Issue.2 , pp. 97-112
    • Hu, T.1    Lin, Z.2    Chen, B.M.3
  • 27
    • 24944522772 scopus 로고    scopus 로고
    • "Conjugate Lyapunov functions for saturated linear systems"
    • T. Hu, R. Goebel, A. R. Teel, and Z. Lin, "Conjugate Lyapunov functions for saturated linear systems," Automatica, vol. 41, no. 11, pp. 1949-1956, 2005.
    • (2005) Automatica , vol.41 , Issue.11 , pp. 1949-1956
    • Hu, T.1    Goebel, R.2    Teel, A.R.3    Lin, Z.4
  • 28
    • 23944477081 scopus 로고    scopus 로고
    • 2 gain and regional analysis for linear systems with anti-windup compensation"
    • in Portland, OR
    • 2 gain and regional analysis for linear systems with anti-windup compensation," in Proc. Amer. Control Conf., Portland, OR, 2005, pp. 3391-3396.
    • (2005) Proc. Amer. Control Conf. , pp. 3391-3396
    • Hu, T.1    Teel, A.R.2    Zaccarian, L.3
  • 29
    • 23944472377 scopus 로고    scopus 로고
    • "Regional anti-windup compensation for linear systems with input saturation"
    • in Portland, OR
    • T. Hu, A. R. Teel, and L. Zaccarian, "Regional anti-windup compensation for linear systems with input saturation," in Proc. Amer. Control Conf., Portland, OR, 2005, pp. 3397-3402.
    • (2005) Proc. Amer. Control Conf. , pp. 3397-3402
    • Hu, T.1    Teel, A.R.2    Zaccarian, L.3
  • 30
    • 84885924509 scopus 로고    scopus 로고
    • Stability and performance for saturated systems via quadratic and non-quadratic Lyapunov functions Dip
    • di Inf., Sist. e Prod., Univ. Rome, Rome, Italy Tech. Rep. RR-06.55
    • T. Hu, A. R. Teel, and L. Zaccarian, Stability and performance for saturated systems via quadratic and non-quadratic Lyapunov functions Dip. di Inf., Sist. e Prod., Univ. Rome, Rome, Italy, 2006, Tech. Rep. RR-06.55.
    • (2006)
    • Hu, T.1    Teel, A.R.2    Zaccarian, L.3
  • 31
    • 37949057361 scopus 로고    scopus 로고
    • 2 performance synthesis"
    • in V. Kapila and K. M. Grigoriadis, Eds. New York: Marcel Dekker
    • 2 performance synthesis," in Actuator Saturation Control, V. Kapila and K. M. Grigoriadis, Eds. New York: Marcel Dekker, 2002, pp. 77-108.
    • (2002) Actuator Saturation Control , pp. 77-108
    • Iwasaki, T.1    Fu, M.2
  • 32
    • 0036990729 scopus 로고    scopus 로고
    • "An LMI method to demonstrate simultaneous stability using non-quadratic polynomial Lyapunov functions"
    • in Las Vegas, NV
    • Z. Jarvis-Wloszek and A. K. Packard, "An LMI method to demonstrate simultaneous stability using non-quadratic polynomial Lyapunov functions," in Proc. Conf. Decision Control, Las Vegas, NV, 2002, pp. 287-292.
    • (2002) Proc. Conf. Decision Control , pp. 287-292
    • Jarvis-Wloszek, Z.1    Packard, A.K.2
  • 33
    • 0032045898 scopus 로고    scopus 로고
    • "Computation of piecewise quadratic Lyapunov functions for hybrid systems"
    • Apr
    • M. Johansson and A. Rantzer, "Computation of piecewise quadratic Lyapunov functions for hybrid systems," IEEE Trans. Autom. Control, vol. 43, no. 4, pp. 555-559, Apr. 1998.
    • (1998) IEEE Trans. Autom. Control , vol.43 , Issue.4 , pp. 555-559
    • Johansson, M.1    Rantzer, A.2
  • 34
    • 0028754144 scopus 로고
    • "A unified framework for the study of anti-windup designs"
    • M. V. Kothare, P. J. Campo, M. Morari, and N. Nett, "A unified framework for the study of anti-windup designs," Automatica, vol. 30, no. 12, pp. 1869-1883, 1994.
    • (1994) Automatica , vol.30 , Issue.12 , pp. 1869-1883
    • Kothare, M.V.1    Campo, P.J.2    Morari, M.3    Nett, N.4
  • 35
    • 0033132830 scopus 로고    scopus 로고
    • "Multiplier theory for stability analysis of anti-windup control systems"
    • M. V. Kothare and M. Morari, "Multiplier theory for stability analysis of anti-windup control systems," Automatica, vol. 35, pp. 917-928, 1999.
    • (1999) Automatica , vol.35 , pp. 917-928
    • Kothare, M.V.1    Morari, M.2
  • 36
    • 0027657413 scopus 로고
    • "Semi-global exponential stabilization of linear systems subject to 'input saturation' via linear feedbacks"
    • Z. Lin and A. Saberi, "Semi-global exponential stabilization of linear systems subject to 'input saturation' via linear feedbacks," Syst. Control Lett., vol. 21, pp. 225-239, 1993.
    • (1993) Syst. Control Lett. , vol.21 , pp. 225-239
    • Lin, Z.1    Saberi, A.2
  • 38
    • 0024702510 scopus 로고
    • "Criteria of asymptotic stability of differential and difference inclusions encountered in control theory"
    • A. P. Molchanov, "Criteria of asymptotic stability of differential and difference inclusions encountered in control theory," Syst. Control Lett., vol. 13, pp. 59-64, 1989.
    • (1989) Syst. Control Lett. , vol.13 , pp. 59-64
    • Molchanov, A.P.1
  • 39
    • 0034542893 scopus 로고    scopus 로고
    • "Synthesis of stabilizing anti-windup controllers using piecewise quadratic Lyapunov functions"
    • in Chicago, IL
    • E. F. Mulder and M. V. Kothare, "Synthesis of stabilizing anti-windup controllers using piecewise quadratic Lyapunov functions," in Proc. Amer. Control Conf., Chicago, IL, 2000, pp. 3239-3243.
    • (2000) Proc. Amer. Control Conf. , pp. 3239-3243
    • Mulder, E.F.1    Kothare, M.V.2
  • 40
    • 0035452398 scopus 로고    scopus 로고
    • "Multivariable anti-windup controller synthesis using linear matrix inequalities"
    • Sep
    • E. F. Mulder, M. V. Kothare, and M. Morari, "Multivariable anti-windup controller synthesis using linear matrix inequalities," Automatica, vol. 37, no. 9, pp. 1407-1416, Sep. 2001.
    • (2001) Automatica , vol.37 , Issue.9 , pp. 1407-1416
    • Mulder, E.F.1    Kothare, M.V.2    Morari, M.3
  • 41
    • 0029377810 scopus 로고
    • "Dynamic compensation method for multivariable control systems saturating actuators"
    • Sep
    • J. K. Park and C. H. Choi, "Dynamic compensation method for multivariable control systems saturating actuators," IEEE Trans. Autom. Control, vol. 40, no. 9, pp. 1635-1640, Sep. 1995.
    • (1995) IEEE Trans. Autom. Control , vol.40 , Issue.9 , pp. 1635-1640
    • Park, J.K.1    Choi, C.H.2
  • 42
    • 0031344399 scopus 로고    scopus 로고
    • "Stability regions for linear systems with saturaing controls via circle and Popov criteria"
    • in San Diego, CA
    • C. Pittet, S. Tarbouriech, and C. Burgat, "Stability regions for linear systems with saturaing controls via circle and Popov criteria," in Proc. 36th IEEE Conf. Decision Control, San Diego, CA, 1997, pp. 4518-4523.
    • (1997) Proc. 36th IEEE Conf. Decision Control , pp. 4518-4523
    • Pittet, C.1    Tarbouriech, S.2    Burgat, C.3
  • 43
    • 0004267646 scopus 로고
    • Princeton, NJ: Princeton Univ. Press
    • R. T. Rockafellar, Convex Analysis. Princeton, NJ: Princeton Univ. Press, 1970.
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 44
    • 0036996247 scopus 로고    scopus 로고
    • "On the robustness of multivariable algebraic loops with sector nonlinearities"
    • in Las Vegas, NV
    • A. Syaichu-Rohman and R. H. Middleton, "On the robustness of multivariable algebraic loops with sector nonlinearities," in Proc. Conf. Decision Control, Las Vegas, NV, 2002, pp. 1054-1059.
    • (2002) Proc. Conf. Decision Control , pp. 1054-1059
    • Syaichu-Rohman, A.1    Middleton, R.H.2
  • 45
    • 0021196599 scopus 로고
    • "An algebraic approach to bounded controllability of linear systems"
    • E. D. Sontag, "An algebraic approach to bounded controllability of linear systems," Int. J. Control, vol. 39, pp. 181-188, 1984.
    • (1984) Int. J. Control , vol.39 , pp. 181-188
    • Sontag, E.D.1
  • 46
    • 0028712602 scopus 로고
    • "A general result on the stabilization of linear systems using bounded controls"
    • Dec
    • H. J. Sussmann, E. D. Sontag, and Y. Yang, "A general result on the stabilization of linear systems using bounded controls," IEEE Trans. Autom. Control, vol. 39, no. 12, pp. 2411-2425, Dec. 1994.
    • (1994) IEEE Trans. Autom. Control , vol.39 , Issue.12 , pp. 2411-2425
    • Sussmann, H.J.1    Sontag, E.D.2    Yang, Y.3
  • 47
    • 37949023301 scopus 로고    scopus 로고
    • "Anti-windup strategy with guaranteed stability for linear systems with amplitude and dynamics restricted actuator"
    • in Stuttgart, Germany
    • S. Tarbouriech, G. Garcia, and P. Langouet, "Anti-windup strategy with guaranteed stability for linear systems with amplitude and dynamics restricted actuator," in Proc. NOLCOS, Stuttgart, Germany, 2004, pp. 1373-1378.
    • (2004) Proc. NOLCOS , pp. 1373-1378
    • Tarbouriech, S.1    Garcia, G.2    Langouet, P.3
  • 48
    • 0026840020 scopus 로고
    • "Global stabilization and restricted tracking for multiple integrators with bounded controls"
    • A. R. Teel, "Global stabilization and restricted tracking for multiple integrators with bounded controls," Syst. Control Lett., vol. 18, pp. 165-171, 1992.
    • (1992) Syst. Control Lett. , vol.18 , pp. 165-171
    • Teel, A.R.1
  • 49
    • 0029221001 scopus 로고
    • "Semi-global stabilizability of linear null controllable systems with input saturation"
    • Jan
    • A. R. Teel, "Semi-global stabilizability of linear null controllable systems with input saturation," IEEE Trans. Autom. Control, vol. 40, no. 1, pp. 96-100, Jan. 1995.
    • (1995) IEEE Trans. Autom. Control , vol.40 , Issue.1 , pp. 96-100
    • Teel, A.R.1
  • 50
    • 84949110350 scopus 로고    scopus 로고
    • 2 anti-windup problem: Its definition and solution"
    • in Brussels, Belgium, Jul
    • 2 anti-windup problem: Its definition and solution," in Proc. 4th Euro. Control Conf., Brussels, Belgium, Jul. 1997.
    • (1997) Proc. 4th Euro. Control Conf.
    • Teel, A.R.1    Kapoor, N.2
  • 51
    • 0015316323 scopus 로고
    • "Global inverse function theorem"
    • Mar
    • F. F. Wu and C. A. Desoer, "Global inverse function theorem," IEEE Trans. Circuits Syst., vol. CAS-19, no. 2, pp. 199-201, Mar. 1972.
    • (1972) IEEE Trans. Circuits Syst. , vol.CAS-19 , Issue.2 , pp. 199-201
    • Wu, F.F.1    Desoer, C.A.2
  • 52
    • 2642584795 scopus 로고    scopus 로고
    • "Anti-windup control design for exponentially unstable LTI systems with actuator saturation"
    • F. Wu and B. Lu, "Anti-windup control design for exponentially unstable LTI systems with actuator saturation," Syst. Control Lett., vol. 52, no. 3-4, pp. 304-322, 2004.
    • (2004) Syst. Control Lett. , vol.52 , Issue.3-4 , pp. 304-322
    • Wu, F.1    Lu, B.2
  • 53
    • 0001360697 scopus 로고    scopus 로고
    • "Piecewise Lyapunov functions for robust stability of linear time-varying systems"
    • L. Xie, S. Shishkin, and M. Fu, "Piecewise Lyapunov functions for robust stability of linear time-varying systems," Syst. Control Lett., vol. 31, pp. 165-171, 1997.
    • (1997) Syst. Control Lett. , vol.31 , pp. 165-171
    • Xie, L.1    Shishkin, S.2    Fu, M.3
  • 54
    • 0036779290 scopus 로고    scopus 로고
    • "A common framework for anti-windup, bumpless transfer and reliable designs"
    • L. Zaccarian and A. R. Teel, "A common framework for anti-windup, bumpless transfer and reliable designs," Automatica, vol. 38, no. 10, pp. 1735-1744, 2002.
    • (2002) Automatica , vol.38 , Issue.10 , pp. 1735-1744
    • Zaccarian, L.1    Teel, A.R.2
  • 55
    • 0028282375 scopus 로고
    • "Non-quadratic Lyapunov functions for robust stability analysis of linear uncertain systems"
    • Jan
    • A. L. Zelentsovsky, "Non-quadratic Lyapunov functions for robust stability analysis of linear uncertain systems," IEEE Trans. Autom. Control, vol. 39, no. 1, pp. 135-138, Jan. 1994.
    • (1994) IEEE Trans. Autom. Control , vol.39 , Issue.1 , pp. 135-138
    • Zelentsovsky, A.L.1


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