手机体育投注平台

Advertisement

Set-Invariance Characterizations and Active Mode Detection for Descriptor Systems

Chapter
  • 3 Downloads
Part of the Springer Theses book series (Springer Theses)

Abstract

This chapter presents a general framework of set-invariance characterizations for discrete-time descriptor systems, and its application to active mode detection  [1, 2] following the research line shown in Fig. 6.1. Among alternative techniques for the computation of invariant sets  [3, 4, 5, 6, 7, 8, 9], we use ultimate boundedness of trajectories to obtain set-invariance characterizations for the systems subject to unknown-but-bounded disturbances  [10].

References

  1. 1.
    Wang Y, Olaru S, Valmorbida G, Puig V, Cembrano G (2017) Robust invariant sets and active mode detection for discrete-time uncertain descriptor systems. In: 56th IEEE conference on decision and control (IEEE-CDC), Melbourne, Australia, pp 5648–5653
  2. 2.
    Wang Y, Olaru S, Valmorbida G, Puig V, Cembrano G (2019) Set-invariance characterizations of discrete-time descriptor systems with application to active mode detection. Automatica 107:255–263
  3. 3.
    Alamo T, Cepeda A, Fiacchini M, Camacho E (2009) Convex invariant sets for discrete-time Lur’e systems. Automatica 45(4):1066–1071
  4. 4.
    Blanchini F, Casagrande D, Miani S (2010) Modal and transition dwell time computation in switching systems: a set-theoretic approach. Automatica 46(9):1477–1482
  5. 5.
    Heidari R, Braslavsky J, Seron M, Haimovich H (2016) Ultimate bound minimisation by state feedback in discrete-time switched linear systems under arbitrary switching. Nonlinear Anal Hybrid Syst 21:84–102
  6. 6.
    Raković S, Kerrigan E, Kouramas K, Mayne D (2005) Invariant approximations of the minimal robust positively invariant set. IEEE Trans Autom Control 50(3):406–410
  7. 7.
    Seron M, De Doná J (2015) On robust stability and set invariance of switched linear parameter varying systems. Int J Control 88(12):2588–2597
  8. 8.
    Seron M, De Doná J (2016) On invariant sets and closed-loop boundedness of Lure-type nonlinear systems by LPV-embedding. Int J Robust Nonlinear Control 26(5):1092–1111
  9. 9.
    Stoican F, Oară C, Hovd M (2015) RPI approximations of the mRPI set characterizing linear dynamics with zonotopic disturbances. In: Developments in model-based optimization and control: distributed control and industrial applications. Springer, pp 361–377
  10. 10.
    Olaru S, De Doná J, Seron M, Stoican F (2010) Positive invariant sets for fault tolerant multisensor control schemes. Int J Control 83(12):2622–2640
  11. 11.
    Kofman E, Seron M, Haimovich H (2008) Control design with guaranteed ultimate bound for perturbed systems. Automatica 44(7):1815–1821
  12. 12.
    Marseglia G, Raimondo D (2017) Active fault diagnosis: a multi-parametric approach. Automatica 79:223–230
  13. 13.
    Stoican F, Olaru S, Seron M, De Doná J (2012) Reference governor design for tracking problems with fault detection guarantees. J Process Control 22(5):829–836
  14. 14.
    Kolmanovsky I, Gilbert E (1998) Theory and computation of disturbance invariant sets for discrete-time linear systems. Math Problems Eng 4(4):317–367
  15. 15.
    Kofman E, Haimovich H, Seron M (2007) A systematic method to obtain ultimate bounds for perturbed systems. Int J Control 80(2):167–178
  16. 16.
    Seron M, De Doná J, Olaru S (2012) Fault tolerant control allowing sensor healthy-to-faulty and faulty-to-healthy transitions. IEEE Trans Autom Control 57(7):1657–1669
  17. 17.
    Dai L (1989) Singular control systems. Springer, Berlin Heidelberg, Germany
  18. 18.
    Zhang L, Lam J, Zhang Q (1999) Lyapunov and Riccati equations of discrete-time descriptor systems. IEEE Trans Autom Control 44(11):2134–2139
  19. 19.
    Gerdin M (2004) Computation of a canonical form for linear differential-algebraic equations. Technical report, Linköping University
  20. 20.
    Blanchini F, Casagrande D, Giordano G, Miani S, Olaru S, Reppa V (2017) Active fault isolation: a duality-based approach via convex programming. SIAM J Control Optim 55(3):1619–1640

Copyright information

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021

Authors and Affiliations

  1. 1.Department of Automatic Control, Institut de Robòtica i Informàtica Industrial, CSIC-UPCUniversitat Politècnica de CatalunyaBarcelonaSpain
  2. 2.College of AutomationHarbin Engineering UniversityHarbinP. R. China
  3. 3.Department of Electrical and Electronic EngineeringThe University of MelbourneMelbourneAustralia

Personalised recommendations