Stability and Closed Trajectory for Second-Order Control Systems with Single-Saturated Input

Chapter

Abstract

In this chapter, based on a new method through defining new equilibrium points, the relationship criterion among equilibrium points is discussed for linear system with saturated inputs. The asymptotic stability of the origin of the linear system in the presence of a single saturation input is analyzed, and the existence equations of closed trajectory is also considered for the same control systems. Finally, characteristics of commutative matrices of MIMO linear systems are considered. And at the same time, we present the simple criterion equations of asymptotic stability of second-order control systems with single-saturated input when \(ABK=BKA\).

Notes

Acknowledgements

This work is Supported by National Key Research and Development Program of China (2017YFF0207400).

References

  1. 1.
    Dugard L, Verrist EI, editors. Stability and control of time-delay systems. Berlin: Springer; 1998. p. 303–10.Google Scholar
  2. 2.
    Henrion D, Tarbouriech S. LMI relaxations for robust stability of linear systems with saturating controls. Automatica. 1999;35:1599–604.MathSciNetCrossRefGoogle Scholar
  3. 3.
    Horisberger HP, Belanger PR. Regulator for linear, time invariant plants with uncertain parameters. IEEE Trans Autom Control. 1976;42:705–8.MathSciNetCrossRefGoogle Scholar
  4. 4.
    Huang L. Stability theory. Beijing: Peking University Press; 1992. p. 235–83.Google Scholar
  5. 5.
    Kapoor N, Daoutidis P. An observer-based anti-windup scheme for nonlinear systems with input constraits. Int J Control. 1999;72(1):18–29.CrossRefGoogle Scholar
  6. 6.
    Lee AW, Hedrick JK. Some new results on closed-loop stability in the presence of control saturation. Int J Control. 1995;62(3):619–51.MathSciNetCrossRefGoogle Scholar
  7. 7.
    Liberzon D, Hespanta JP, Morse AS. Stability of switched systems: a Lie-algebraic condition. Syst Control Lett North-Holland. 1999;37:117–22.MathSciNetCrossRefGoogle Scholar
  8. 8.
    Mareada KS, Balakrishan J. A common Lyapunov function for stable LTI systems with commuting A-martices. IEEE Trans Autom Control. 1994;39(12):2469–71.CrossRefGoogle Scholar
  9. 9.
    Mancilla-Aguilar JL, Garcia RA. A converse Lyapunov theorem for nonlinear switched systems. Syst Control Lett North-Holland. 2000;41(1):69–71.MathSciNetMATHGoogle Scholar
  10. 10.
    Molchanov AP, Pyatnitskiy YS. Criteria of asymptotic stability of differential and difference inclusions encountered in control theory. Syst Control Lett North-Holland. 1989;13:59–64.MathSciNetCrossRefGoogle Scholar
  11. 11.
    Polanski K. On absolute stability analysis by polyhedric Lypunov functions. Automatica. 2000;36:573–8.MathSciNetCrossRefGoogle Scholar
  12. 12.
    Scibile L, Kouvaritakis BIF. Stability region for a class of open-loop unstable linear systems: theory and application. Automatica. 2000;36(1):37–44.MathSciNetCrossRefGoogle Scholar
  13. 13.
    Sontag ED, Sussmann HJ. Nonlinear output feedback design for linear systems with saturated control. In: Proceeding of 29th conference on decision and control; 1990. vol. 45(5). p. 719–721.Google Scholar
  14. 14.
    Tatsushi, Yasuyuki F. Two conditions concerning common quadratic Lyapunov functions for linear systems. IEEE Trans Autom Control. 1997;42(5):750–761.Google Scholar
  15. 15.
    Tarbouriech S, Gomes da JM. Synthesis of controllers for continuous-times delay systems with saturated control via LMIs. IEEE Trans Autom Control. 2000;45(1):105–11.Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Key Laboratory of Complex System Intelligent Control and Decision, School of AutomationBeijing Institute of TechnologyBeijingChina
  2. 2.Department of Cardiovascular Internal Medicine of Nanlou Branch, National Clinical Research Center for Geriatric DiseasesChinese PLA General HospitalBeijingChina

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