http://iet.metastore.ingenta.com
1887

Input-delay approach to sampled-data control of polynomial systems based on a sum-of-square analysis

Input-delay approach to sampled-data control of polynomial systems based on a sum-of-square analysis

For access to this article, please select a purchase option:

Buy article PDF
$19.95
(plus tax if applicable)
Buy Knowledge Pack
10 articles for $120.00
(plus taxes if applicable)

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Name:*
Email:*
Your details
Name:*
Email:*
Department:*
Why are you recommending this title?
Select reason:
 
 
 
 
 
IET Control Theory & Applications — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

In this study, the authors develop an stabilisation condition for polynomial sampled-data control systems with respect to an external disturbance. Generally, continuous-time and sampled state variables are mixed in polynomial sampled-data control systems, which is the main drawback to numerically solving the stabilisation conditions of these control systems. To overcome this drawback, this study proposes novel stabilisation conditions that address the mixed-states problem by casting the mixed states as a time-varying uncertainty. The stabilisation conditions are derived from a newly proposed polynomial time-dependent Lyapunov–Krasovskii functional and are represented as a sum-of-squares, which can be solved using existing numerical solvers. Some additional slack variables are further introduced to relax the conservativeness of the authors' proposed approach. Finally, some simulation examples are provided to demonstrate the effectiveness of their approach.

References

    1. 1)
      • 1. Chesi, G.: ‘Computing output feedback controllers to enlarge the domain of attraction in polynomial systems’, IEEE Trans. Autom. Control, 2004, 49, (10), pp. 18461850.
    2. 2)
      • 2. Ebenbauer, C., Renz, J., Allgower, F.: ‘Polynomial feedback and observer design using nonquadratic Lyapunov functions’. Proc. Joint IEEE Conf. Decision and Control and European Control Conf., 2005, pp. 75877592.
    3. 3)
      • 3. Ichihara, H.: ‘Optimal control for polynomial systems using matrix sum of squares relaxations’, IEEE Trans. Autom. Control, 2009, 54, (5), pp. 10481053.
    4. 4)
      • 4. Jarvis-Wloszek, Z., Feeley, R., Tan, W., et al: ‘Some controls applications of sum of squares programming’. Proc. IEEE Conf. Decision and Control, 2003, pp. 46764681.
    5. 5)
      • 5. Kim, H.S., Park, J.B., Joo, Y.H.: ‘Further relaxed stability conditions for continuous-time polynomial fuzzy system based on polynomial fuzzy Lyapunov function’. FUZZ-IEEE, 2012, pp. 18281832.
    6. 6)
      • 6. Prajna, S., Papachristodoulou, A., Fen, W.: ‘Nonlinear control synthesis by sum of squares optimization: a Lyapunov-based approach’. Proc. Asian Control Conf., 2004, pp. 157165.
    7. 7)
      • 7. Saat, S., Huang, D., Nguang, S.K., et al: ‘Nonlinear state feedback control for a class of polynomial nonlinear discrete-time systems with norm-bounded uncertainties: an integrator approach’, J. Franklin Inst., 2013, 350, (7), pp. 17391752.
    8. 8)
      • 8. Saat, S., Nguang, S.K.: ‘Nonlinear H output feedback control with integrator for polynomial discrete-time systems’, Int. J. Robust Nonlinear Control, 2013, 25, (7), pp. 10511065.
    9. 9)
      • 9. Ataei-Esfahani, A., Wang, Q.: ‘Nonlinear control design of a hypersonic aircraft using sum-of-squares method’. American Control Conf., 2007, pp. 52785283.
    10. 10)
      • 10. Tayebi, A., McGilvray, S.: ‘Attitude stabilization of a VTOL quadrotor aircraft’, IEEE Trans. Control Syst. Technol., 2006, 14, (3), pp. 562571.
    11. 11)
      • 11. Krstic, M., Kanellakopoulos, I., Kokotovic, P.V.: ‘Nonlinear and adaptive control design’ (Wiley, NY, 1995).
    12. 12)
      • 12. Lee, H.J., Park, J.B., Joo, Y.H.: ‘Robust fuzzy control of nonlinear systems with parametric uncertainties’, IEEE Trans. Fuzzy Syst., 2001, 9, (2), pp. 369379.
    13. 13)
      • 13. Ichihara, H., Nobuyama, E.: ‘How to use SOSTOOLS together with matrix patch’. Proc. SICE Annual Conf., 2005, pp. 38063810.
    14. 14)
      • 14. Prajna, S., Papachristodoulou, A., Seiler, P., et al: ‘SOSTOOLS: sum of squares optimization toolbox for MATLAB’ (California Inst. Tech., 2004).
    15. 15)
      • 15. Zhang, X.M., Han, Q.L., Yu, X.: ‘Survey on recent advances in networked control system’, IEEE Trans. Ind. Inf., 2016, 12, (5), pp. 17401752.
    16. 16)
      • 16. Lee, D.H., Joo, Y.H.: ‘LMI-based robust sampled-data stabilization of polytopic LTI systems: a truncated power series expansion approach’, Int. J. Control Autom. Syst., 2015, 13, (2), pp. 284291.
    17. 17)
      • 17. Kim, D.W., Lee, H.J., Tomizuka, M.: ‘Fuzzy stabilization of nonlinear systems under sampled-data feedback: an exact discrete-time model approach’, IEEE Trans. Fuzzy Syst., 2010, 18, (2), pp. 251260.
    18. 18)
      • 18. Kim, D.W., Lee, H.J.: ‘Sampled-data observer-based output-feedback fuzzy stabilization of nonlinear systems: exact discrete-time design approach’, Fuzzy Sets Syst., 2012, 201, pp. 2039.
    19. 19)
      • 19. Kim, H.J., Koo, G.B., Park, J.B., et al: ‘Decentralized sampled-data H fuzzy filter for nonlinear large-scale systems’, Fuzzy Sets Syst., 2015, 273, pp. 6886.
    20. 20)
      • 20. Fridman, E., Seuret, A., Richard, J.P.: ‘Robust sampled-data stabilization of linear systems: an input delay approach’, Automatica, 2004, 40, (8), pp. 14411446.
    21. 21)
      • 21. Fridman, E.: ‘A refined input delay approach to sampled-data control’, Automatica, 2010, 46, (2), pp. 421427.
    22. 22)
      • 22. Hu, L.S., Bai, T., Shi, P., et al: ‘Sampled-data control of networked linear control systems’, Automatica, 2007, 43, pp. 903911.
    23. 23)
      • 23. Lu, J.G., Hill, D.J.: ‘Global asymptotical synchronization of chaotic Lur'e systems using sampled data: a linear matrix inequality approach’, IEEE Trans. Circuit Syst., 2008, 55, (6), pp. 586590.
    24. 24)
      • 24. Naghshtabrizi, P., Hespanha, J.P., Teel, A.R.: ‘Exponential stability of impulsive systems with application to uncertain sampled-data systems’, Syst. Control Lett., 2008, 57, pp. 378385.
    25. 25)
      • 25. Khalil, H.K.: ‘Nonlinear systems’ (Prentice-Hall, NJ, 2001).
    26. 26)
      • 26. Lam, H.K.: ‘Stabilization of nonlinear systems using sampled-data output-feedback fuzzy controller based on polynomial-fuzzy-model-based control approach’, IEEE Trans. Syst. Man Cybern., 2012, 42, (1), pp. 258267.
    27. 27)
      • 27. Zhang, X.M., Han, Q.L.: ‘Event-based H filtering for sampled-data systems’, Automatica, 2015, 51, pp. 5569.
    28. 28)
      • 28. Lofberg, J.: ‘YALMIP : a toolbox for modeling and optimization in MATLAB’. IEEE Int. Symp. Computer Aided Control System Design, 2004, pp. 284289.
    29. 29)
      • 29. Strum, J.F.: ‘Using SeDuMi 1.02, a MATLAB tool-box for optimization over symmetric cones’, Opt. Method Soft., 1999, 11, pp. 625653.
    30. 30)
      • 30. Koo, G.B., Park, J.B., Joo, Y.H.: ‘LMI condition for sampled-data fuzzy control of nonlinear systems’, IET Electr. Lett., 2015, 51, (1), pp. 2931.
    31. 31)
      • 31. Tanaka, K, Ikeda, T., Wang, H.O.: ‘Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: quadratic stabilizbility, H control theory, and linear matrix inequality’, IEEE Trans. Fuzzy Syst., 1996, 40, (1), pp. 113.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2016.1037
Loading

Related content

content/journals/10.1049/iet-cta.2016.1037
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
This is a required field
Please enter a valid email address