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A new estimate of DoA for saturated systems and its applications

  • Research Center of Early Warning & Detection, CETC 38, Hefei 230088, China

Funds:  National Key Project of Science and Technology Supported Plan(2011BAH24B06).
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https://doi.org/10.3969/j.issn.0253-2778.2015.04.001
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  • Corresponding author: SHANG Weike(corresponding author), male, born in 1984,PhD/Engineer. Research field: Stochastic system, radar signal processing. E-mail: wufo@mail.ustc.edu.cn
  • Received Date: 25 September 2014
  • Accepted Date: 14 November 2014
  • Rev Recd Date: 14 November 2014
  • Publish Date: 30 April 2015
    Abstract

  • Abstract

    A new method for estimating the domain of attraction(DoA) for saturated systems was presented. Compared with the existing results, the advantage of the new result is mainly twofold: ① It does not include any product by the system matrix and the Lyapunov matrix; ② It does not result in heavy computing cost. It will be seen that these features are essentially important in system analysis. For comparison, the new result was extended to uncertain saturated systems, which shows that it leads to less conservativeness. Numerical examples verify the correctness of the conclusion.

    Abstract

    A new method for estimating the domain of attraction(DoA) for saturated systems was presented. Compared with the existing results, the advantage of the new result is mainly twofold: ① It does not include any product by the system matrix and the Lyapunov matrix; ② It does not result in heavy computing cost. It will be seen that these features are essentially important in system analysis. For comparison, the new result was extended to uncertain saturated systems, which shows that it leads to less conservativeness. Numerical examples verify the correctness of the conclusion.
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    • References(12)
  • [1]
    GilbertE G, Tan K T. Linear systems with state and control constraints: The theory and application of maximal output admissible sets[J]. IEEE Transactions on Automatic Control, 1991, 36(9): 1008-1020.
    [2]
    Khalil H K. Nonlinear Systems[M]. Upper Saddle River: Prentice-Hall, 1996.
    [3]
    Pittet C, Tarbouriech S, Burdat C. Stability regions for linear systems with saturating controls via circle and Popov criteria[C]// Proceedings of the 36th IEEE Conference on Decision & Control. San Diego, USA: IEEE Press, 1997: 4518-4523.
    [4]
    Hu T S, Lin Z L. Control Systems with Actuator Saturation: Analysis and Design[M]. Berlin: Birkhuser, 2001.
    [5]
    Hu T S, Lin Z L, Chen B M. Analysis and design for discrete-time linear systems subject to actuator saturation[J]. Systems & Control Letters, 2002, 45(2): 97-112.
    [6]
    Hu T S, Lin Z L, Chen B M. An analysis and design method for linear systems subject to actuator saturation and disturbance[J]. Automatica, 2002, 38(2): 351-359.
    [7]
    Cao Y Y, Lin Z L. Stability analysis of discrete-time systems with actuator saturation by a saturation-dependent Lyapunov function[J]. Automatica, 2003, 39(7): 1235-1241.
    [8]
    Alamo T, Cepeda A, Limon D, et al. A new concept of invariance for saturated systems[J]. Automatica, 2006, 42(9): 1515-1521.
    [9]
    Lu L, Lin Z L. A switching anti-windup design using multiple Lyapunov functions[J]. IEEE Transactions on Automatic Control, 2009, 55(1): 142-148.
    [10]
    Daafouz J, Bernussou J. Parameter dependent Lyapunov functions for discrete time systems with time varying parametric uncertainties[J]. Systems & Control Letters, 2001, 43(5): 355-359.
    [11]
    CaoY Y, Lin Z L. A descriptor system approach to robust stability analysis and controller synthesis[J]. IEEE Transactions on Automatic Control, 2004, 49(11): 2081-2084.
    [12]
    de Oliveira M C, Bernussou J, Geromel J C. A new discrete-time robust stability condition[J]. Systems & Control Letters, 1999, 37(4): 261-265.)
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    [1]
    GilbertE G, Tan K T. Linear systems with state and control constraints: The theory and application of maximal output admissible sets[J]. IEEE Transactions on Automatic Control, 1991, 36(9): 1008-1020.
    [2]
    Khalil H K. Nonlinear Systems[M]. Upper Saddle River: Prentice-Hall, 1996.
    [3]
    Pittet C, Tarbouriech S, Burdat C. Stability regions for linear systems with saturating controls via circle and Popov criteria[C]// Proceedings of the 36th IEEE Conference on Decision & Control. San Diego, USA: IEEE Press, 1997: 4518-4523.
    [4]
    Hu T S, Lin Z L. Control Systems with Actuator Saturation: Analysis and Design[M]. Berlin: Birkhuser, 2001.
    [5]
    Hu T S, Lin Z L, Chen B M. Analysis and design for discrete-time linear systems subject to actuator saturation[J]. Systems & Control Letters, 2002, 45(2): 97-112.
    [6]
    Hu T S, Lin Z L, Chen B M. An analysis and design method for linear systems subject to actuator saturation and disturbance[J]. Automatica, 2002, 38(2): 351-359.
    [7]
    Cao Y Y, Lin Z L. Stability analysis of discrete-time systems with actuator saturation by a saturation-dependent Lyapunov function[J]. Automatica, 2003, 39(7): 1235-1241.
    [8]
    Alamo T, Cepeda A, Limon D, et al. A new concept of invariance for saturated systems[J]. Automatica, 2006, 42(9): 1515-1521.
    [9]
    Lu L, Lin Z L. A switching anti-windup design using multiple Lyapunov functions[J]. IEEE Transactions on Automatic Control, 2009, 55(1): 142-148.
    [10]
    Daafouz J, Bernussou J. Parameter dependent Lyapunov functions for discrete time systems with time varying parametric uncertainties[J]. Systems & Control Letters, 2001, 43(5): 355-359.
    [11]
    CaoY Y, Lin Z L. A descriptor system approach to robust stability analysis and controller synthesis[J]. IEEE Transactions on Automatic Control, 2004, 49(11): 2081-2084.
    [12]
    de Oliveira M C, Bernussou J, Geromel J C. A new discrete-time robust stability condition[J]. Systems & Control Letters, 1999, 37(4): 261-265.)
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