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Stabilisation of discrete-time switched positive linear systems via time- and state-dependent switching laws

Stabilisation of discrete-time switched positive linear systems via time- and state-dependent switching laws

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This study investigates the stabilisation problem of discrete-time switched positive linear systems by means of piecewise linear copositive Lyapunov functions. Two stabilisation strategies are designed under time- and state-dependent switching cases, respectively. The former case aims at determining an upper bound of the minimum dwell time to guarantee that the underlying system is stable for any switching signal with dwell time greater than this bound. The latter case is focused on deriving a state-dependent switching law stabilising the underlying system from the solution of a family of so-called linear copositive Lyapunov–Metzler inequalities. In each case, a sufficient stabilisation condition is given first, then based on which an associated guaranteed cost is further proposed. A practical system derived from the distributed power control in communication networks is given to illustrate the effectiveness and applicability of the theoretical results.

Inspec keywords: time-varying systems; piecewise linear techniques; linear systems; distributed control; Lyapunov methods; stability; power control; discrete time systems

Other keywords: discrete-time switched positive linear systems; stabilisation problem; time-dependent switching laws; distributed power control; piecewise linear copositive Lyapunov functions; communication networks; state-dependent switching laws; linear copositive Lyapunov-Metzler inequalities

Subjects: Control system analysis and synthesis methods; Discrete control systems; Power and energy control; Stability in control theory; Time-varying control systems

References

    1. 1)
    2. 2)
    3. 3)
    4. 4)
    5. 5)
    6. 6)
      • O. Mason , V.S. Bokharaie , R. Shorten . (2009) Stability and D-stability for switched positive systems, Positive systems.
    7. 7)
      • T. Kaczorek . (2002) Positive 1D and 2D systems.
    8. 8)
    9. 9)
    10. 10)
    11. 11)
    12. 12)
    13. 13)
    14. 14)
      • G. James , V. Rumchev . Stability of positive linear discrete-time systems. Bull. Pol. Acad. Sci. Tech. Sci. , 1 , 1 - 8
    15. 15)
    16. 16)
    17. 17)
    18. 18)
    19. 19)
    20. 20)
      • Zappavigna, A., Colaneri, P., Geromel, J., Middleton, R.: `Stabilization of continuous-time switched linear positive systems', Proc. America Control Conference, 2010, Baltimore, America, p. 3275–3280.
    21. 21)
    22. 22)
      • R.A. Decarlo , M.S. Branicky , S. Pettersson , B. Lennartson . Perspective and results on the stability and stabilizability of hybrid systems. Proc. IEEE , 1069 - 1081
    23. 23)
    24. 24)
      • Zappavigna, A., Colaneri, P., Geromel, J., Shorten, R.: `Dwell time analysis for continuous-time switched linear positive systems', Proc. the America Control Conference, 2010, Baltimore, America, p. 6256–6261.
    25. 25)
    26. 26)
    27. 27)
    28. 28)
      • D. Liberzon . (2003) Switching in systems and control.
    29. 29)
    30. 30)
      • X. Liu , W. Yu , L. Wang . Stability analysis of positive systems with bounded time-varying delays. IEEE Trans. Autom. Control , 7 , 600 - 604
    31. 31)
    32. 32)
      • M. Twardy . On the alternative stability criterion for positive systems. Bull. Pol. Acad. Sci. Tech. Sci. , 4 , 379 - 383
    33. 33)
    34. 34)
    35. 35)
      • Paul, A., Akar, M., Mitra, U., Safonov, M.G.: `A switched system model for stability analysis of distributed power control algorithms for cellular communications', Proc. 2004 American Control Conference, 2004, Boston, Massachusetts.
    36. 36)
    37. 37)
      • A. Berman , R.J. Plemmons . (1994) Nonnegative matrices in the mathematical sciences.
    38. 38)
      • L. Farina , S. Rinaldi . (2000) Positive linear systems: theory and applications.
    39. 39)
      • W. Mitkowski . Dynamical properties of Metzler systems. Bull. Pol. Acad. Sci. Tech. Sci. , 4 , 309 - 312
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