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Dwell-time approach to ℒ2-induced gain analysis of discrete-time switched systems subject to actuator saturation

Dwell-time approach to ℒ2-induced gain analysis of discrete-time switched systems subject to actuator saturation

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This study investigates ℒ2-induced gain from the input disturbance to output of discrete-time switched linear systems subject to actuator saturation. With the state feedback gains adopted beforehand, the authors establish the linear matrix inequalities formulation which estimates the restricted ℒ2-induced gain for this class of switched systems by dwell-time approach. Then the authors investigate the influence of parameter variations on the restricted ℒ2-induced gain, and present a state feedback design method for a fixed dwell time and an upper bound of restricted ℒ2-induced gain. In addition, the authors investigate the qualitative relationship between disturbances rejection capability and dwell time. A numerical example is provided to illustrate the effectiveness of our obtained results.

References

    1. 1)
      • 41. Löfberg, J.: ‘YALMIP: a toolbox for modeling and optimization in MATLAB’. Proc. CACSD Conf., Taipei, Taiwan, 2004, pp. 284289.
    2. 2)
      • 13. Zhai, G., Hu, B., Yasuda, K., Michel, A.N.: ‘Disturbance attenuation properties of time-controlled switched systems’, J. Franklin Inst., 2001, 338, pp. 765779.
    3. 3)
      • 15. Roberson, D.G., Stilwell, D.J.: ‘2 gain of periodic linear switched systems: fast switching behavior’, IEEE Trans. Autom. Control, 2009, 54, (7), pp. 16321637.
    4. 4)
      • 9. Zhai, G., Hu, B., Yasuda, K., Michel, A.N.: ‘Qualitative analysis of discrete-time switched systems’. Proc. American Control Conf., Orlando, USA, 2002, pp. 18801885.
    5. 5)
      • 29. Soodavi, M., Ghaisari, J., Sheikholeslam, F.: ‘2 gain analysis for switched systems with state-dependent switching signal’, IET Proc., Control Theory Appl., 2011, 5, (13), pp. 15231527.
    6. 6)
      • 17. Hespanha, J.P.: ‘2-induced gains of switched linear systems’, in Blondel, V., Megretski, A., (Eds.): ‘Unsolved problems in mathematical systems and control theory’ (Princeton University Press, 2004), pp. 131133.
    7. 7)
      • 12. van der Schaft, A.J.: ‘2-Gain and passivity techniques in nonlinear control’ (Springer-Verlag, 2000, 2nd edn.).
    8. 8)
      • 40. Rugh, W.J.: Linear systems theory (Prentice-Hall, 1996, 2nd edn.).
    9. 9)
      • 28. Wada, N., Oomoto, T., Saeki, M.: ‘2-gain analysis of discrete-time systems with saturation nonlinearity using parameter dependent Lyapunov function’. Proc. 43th IEEE Conf. Decision and Control, Atlantis, Paradise Island, Bahamas, 2004, pp. 19521957.
    10. 10)
      • 2. Sun, Z., Ge, S.S.: ‘Switched linear systems: control and design’ (Springer-Verlag, 2005).
    11. 11)
      • 36. Chen, Y., Fei, S., Zhang, K., Yu, L.: ‘Control of switched linear systems with actuator saturation and its applications’, Math. Comput. Model., 2012, 56, (1–2), pp. 1426.
    12. 12)
      • 10. Wu, A.G., Feng, G., Duan, G.R., Gao, H.: ‘Stabilising slow-switching laws for switched discrete-time linear systems’, IET Proc., Control Theory Appl., 2011, 5, (16), pp. 18431858.
    13. 13)
      • 19. Margaliot, M., Hespanha, J.P.: ‘Root-mean-square gains of switched linear systems: a variational approach’, Automatica, 2008, 44, (9), pp. 23982402.
    14. 14)
      • 26. Hu, T., Lin, Z.: ‘Control systems with actuator saturation: analysis and design’ (Birkhäuser, 2001).
    15. 15)
      • 5. Zhai, S., Yang, X.S.: ‘Stability analysis of feedback switched systems with state and switching delays’, IMA J. Math. Control Inf., 2012, doi:10.1093/imamci/dns010.
    16. 16)
      • 7. Dehghan, M., Ong, C.J.: ‘Discrete-time switching linear system with constraints: characterization and computation of invariant sets under dwell-time consideration’, Automatica, 2012, 48, (5), pp. 964969.
    17. 17)
      • 38. Lu, L., Lin, Z.: ‘Design of switched linear systems in the presence of actuator saturation’, IEEE Trans. Autom. Control, 2008, 53, (6), pp. 15361542.
    18. 18)
      • 32. Zhang, X., Zhao, J., Dimirovski, G.M.: ‘2-gain analysis and control synthesis of uncertain switched linear systems subject to actuator saturation’, Int. J. Syst. Sci., 2012, 43, (4), pp. 731740.
    19. 19)
      • 34. Benzaouia, A., Akhrif, O., Saydy, L.: ‘Stabilisation and control synthesis of switching systems subject to actuator saturation’, Int. J. Syst. Sci., 2010, 41, (4), pp. 397409.
    20. 20)
      • 35. Benzaouia, A., Saydy, L., Akhrif, O.: ‘Stability and control synthesis of switched systems subject to actuator saturation’. Proc. American Control Conf., Boston, USA, 2004, pp. 58185823.
    21. 21)
      • 25. Cai, C.: ‘Dwell-time approach to input-output stability properties for a class of discrete-time dynamical systems’, Syst. Control Lett., 2011, 60, pp. 383389.
    22. 22)
      • 18. Hespanha, J.P.: ‘Root-mean-square gains of switched linear systems’, IEEE Trans. Autom. Control, 2003, 48, (11), pp. 20402045.
    23. 23)
      • 33. Ni, W., Cheng, D.: ‘Control of switched linear systems with input saturation’, Int. J. Syst. Sci., 2010, 41, (9), pp. 10571065.
    24. 24)
      • 27. Hu, T., Lin, Z., Chen, B.M.: ‘Analysis and design for discrete-time linear systems subject to actuator saturation’, Syst. Control Lett., 2002, 45, (2), pp. 97112.
    25. 25)
      • 24. Colaneri, P., Bolzern, P., Geromel, J.C.: ‘Root mean square gain of discrete-time switched linear systems under dwell time constraints’, Automatica, 2011, 47, (8), pp. 16771684.
    26. 26)
      • 4. Lin, H., Antsaklis, P.J.: ‘Stability and stabilizability of switched linear systems: a survey of recent results’, IEEE Trans. Autom. Control, 2009, 54, (2), pp. 308322.
    27. 27)
      • 8. Zhang, L., Shi, P., Basin, M.: ‘Robust stability and stabilisation of uncertain switched linear discrete time-delay systemsIET Proc., Control Theory Appl., 2008, 2, (7), pp. 606614.
    28. 28)
      • 14. Xie, D., Wang, L., Hao, F., Xie, G.: ‘LMI approach to ℒ2 gain analysis and control synthesis of uncertain switched systems’, IEE Proc., Control Theory Appl., 2004, 151, (1), pp. 2128.
    29. 29)
      • 23. Lee, J., Dullerud, G.E.: ‘Optimal disturbance attenuation for discrete-time switched and Markovian jump linear systems’, SIAM J. Control Optim., 2006, 45, (4), pp. 1329C1358.
    30. 30)
      • 21. Hirata, K., Hespanha, J.P.: ‘2-induiced gain analysis of switched linear systems via finitely parameterized storage functions’. Proc. American Control Conf., Baltimore, USA, 2010, pp. 40644069.
    31. 31)
      • 37. Chen, Y., Fei, S., Zhang, K., Fu, Z.: ‘Control synthesis of discrete-time switched linear systems with input saturation based on minimum dwell time approach’, Circuits Syst. Signal Process., 2012, 31, (2), pp. 779795.
    32. 32)
      • 1. Liberzon, D.: ‘Switching in systems and control’ (Birkhäuser, 2003).
    33. 33)
      • 31. Zhang, X., Zhao, J., Dimirovski, G.M.: ‘2-Gain analysis and control synthesis of uncertain discrete-time switched linear systems with time delay and actuator saturation’, Int. J. Control, 2011, 84, (10), pp. 17461758.
    34. 34)
      • 3. Shorten, R., Wirth, F., Mason, O., Wulff, K., King, C.: ‘Stability criteria for switched and hybrid systems’, SIAM Rev., 2007, 49, (4), pp. 545592.
    35. 35)
      • 6. Dehghan, M., Ong, C.J., Chen, C.Y.: ‘Characterization and computation of robust invariant sets for switching systems under dwell-time consideration’. Proc. 50th IEEE Conf. Decision and Control and European Control Conf., Orlando, USA, 2011, pp. 11661171.
    36. 36)
      • 11. Ding, D.W., Yang, G.H.: ‘H static output feedback control for discrete-time switched linear systems with average dwell time’, IET Proc., Control Theory Appl., 2010, 4, (3), pp. 381390.
    37. 37)
      • 22. Geromel, J.C., Colaneri, P.: ‘H and dwell time specifications of continuous-time switched linear systems’, IEEE Trans. Autom. Control, 2010, 55, (1), pp. 207212.
    38. 38)
      • 16. Zhao, J., Hill, D.J.: ‘On stability and ℒ2 gain and H control for switched systems’, Automatica, 2008, 44, pp. 12201232.
    39. 39)
      • 20. Hirata, K., Hespanha, J.P.: ‘2-induiced gain analysis for a class of switched systems’. Proc. 48th IEEE Conf. Decision and Control, Shanghai, China, 2009, pp. 21382143.
    40. 40)
      • 39. Lu, L., Lin, Z., Fang, H.: ‘2 gain analysis for a class of switched systems’, Automatica, 2009, 45, (4), pp. 965972.
    41. 41)
      • 30. Ma, Y.M., Yang, G.H.: ‘Disturbance rejection of switched discrete-time systems with saturation nonlinearity’. Proc. 46th IEEE Conf. Decision and Control, New Orleans, USA, 2007, pp. 31703175.
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