access icon free Results on finite-time boundedness and finite-time control of non-linear quadratic systems subject to norm-bounded disturbances

The present study investigates the synthesis of sufficient conditions for finite-time boundedness and stabilisation of non-linear quadratic systems with exogenous disturbances. For this purpose, the usefulness of combining the notion of annihilator with a version of Finsler's lemma has been investigated. The obtained design conditions are expressed in terms of a set of state-dependent linear matrix inequalities. Several numerical examples are given to show the effectiveness of the authors' approach.

Inspec keywords: quadratic programming; nonlinear control systems; control system synthesis; linear matrix inequalities

Other keywords: normbounded disturbances; Finslers lemma; state-dependent linear matrix inequalities; finite time boundedness; finite-time control; nonlinear quadratic systems; design conditions

Subjects: Control system analysis and synthesis methods; Nonlinear control systems; Optimisation techniques; Algebra

References

    1. 1)
      • 1. ElBsat, M. (2012). ‘Finite-time control and estimation of nonlinear systems with disturbance attenuation’. PhD thesis, Marquette University, Milwaukee, Wisconsin.
    2. 2)
      • 8. Amato, F., Ariola, M., Abdallah, C., et al: ‘Finite-time control for uncertain linear systems with disturbance inputs’. American Control Conf., San Diego, USA, 1999, pp. 17761780.
    3. 3)
      • 9. Figalli, G., La Cava, M., Tomasi, L.: ‘An optimal feedback control for a bilinear model of induction motor drives’, Int. J. Control, 1984, 39, (5), pp. 10071016.
    4. 4)
      • 14. Bhiri, B., Delattre, C., Zasadzinski, M., et al: ‘Finite time H controller design based on finite time H functional filter for linear continuous systems’. Int. Conf. on Systems and Control, Sousse, Tunisia, 2015, pp. 460465.
    5. 5)
      • 25. Trofino, A., Dezuo, T.: ‘LMI stability conditions for uncertain rational nonlinear systems’, Int. J. Robust Nonlinear Control, 2014, 24, (18), pp. 31243169.
    6. 6)
      • 10. Reduced order bilinear models for distillation columns', Automatica, 1978, 14, (4), pp. 345355.
    7. 7)
      • 18. ElBsat, M., Yaz, E.: ‘Mixed criteria control design with finite-time boundedness and H property for a class of discrete-time nonlinear systems’. IEEE Conf. on Decision and Control and European Control Conf., Orlando, USA, 2011, pp. 35203525.
    8. 8)
      • 13. Delattre, C., Bhiri, B., Zemouche, A., et al: ‘Finite-time H functional filter design for a class of descriptor linear systems’. IEEE Mediterranean Conf. on Control and Automation, Palermo, Italy, 2014.
    9. 9)
      • 20. Boyd, S., El Ghaoui, L., Féron, E., et al: ‘Linear matrix inequalities in systems and control theory’ (SIAM, Philadelphia, 1994).
    10. 10)
      • 6. Bhat, S., Bernstein, D.: ‘Continuous finite-time stabilization of the translational and rotational double integrators’, IEEE Trans. Autom. Control, 1998, 43, (5), pp. 678682.
    11. 11)
      • 21. Meng, Q., Shen, Y.: ‘Finite-time H control for linear continuous system with norm-bounded disturbance’, Commun. Nonlinear Sci. Numer. Simul., 2009, 14, (4), pp. 10431049.
    12. 12)
      • 7. Moulay, E.: ‘Une contribution à l'etude de la stabilité en temps fini et de la stabilisation’. PhD thesis, Ecole Centrale de Lille, Lille, France, 2005.
    13. 13)
      • 22. Moulay, E., Perruquetti, W.: ‘Finite time stability conditions for non-autonomous continuous systems’, Int. J. Control, 2008, 81, (5), pp. 797803.
    14. 14)
      • 3. Weiss, L., Infante, E.: ‘On the stability of systems defined over a finite time interval’, Proc. Natl. Acad. Sci. USA, 1965, 54, (1), pp. 4448.
    15. 15)
      • 2. Dorato, P.: ‘Short-time stability’, IRE Trans. Autom. Control, 1961, 6, (1), p. 86.
    16. 16)
      • 5. Amato, F., Ambrosino, R., Ariola, M., et al: ‘Finite-time stability and control’ (Springer-Verlag, London, 2014) (Lecture Notes in Control and Information Sciences, 453).
    17. 17)
      • 24. Kokotović, P.V., Kanellakopoulos, I., Morse, A.: ‘Adaptive feedback linearization of nonlinear systems’, in Kokotović, P.V. (Ed.): ‘Foundations of adaptive control’ (Springer, New York, 1991) pp. 309346.
    18. 18)
      • 12. Amato, F., Ariola, M., Dorato, P.: ‘Finite-time control of linear systems subject to parametric uncertainties and disturbances’, Automatica, 2001, 37, (9), pp. 14591463.
    19. 19)
      • 17. Chen, F., Xu, S., Zou, Y., et al: ‘Finite-time boundedness and stabilisation for a class of non-linear quadratic time-delay systems with disturbances’, IET Control Theory Applic., 2013, 7, (13), pp. 16831688.
    20. 20)
      • 4. Weiss, L., Infante, E.: ‘Finite time stability under perturbing forces and on product spaces’, IEEE Trans. Autom. Control, 1967, 12, (1), pp. 5459.
    21. 21)
      • 15. Bhiri, B., Delattre, C., Zasadzinski, M., et al: ‘Finite time H control via dynamic output feedback for linear continuous systems with norm-bounded disturbances’. European Control Conf., Linz, Austria, 2015.
    22. 22)
      • 11. Roy, A., Solimano, F.: ‘Global stability and oscillations in classical Lotka–Volterra loops’, J. Math. Biol., 1987, 24, (6), pp. 603616.
    23. 23)
      • 23. Amato, F., Ariola, M., Cosentino, C.: ‘Finite-time stability of linear time-varying systems: analysis and controller design’, IEEE Trans. Autom. Control, 2010, 55, (4), pp. 10031008.
    24. 24)
      • 19. Amato, F., Ambrosino, R., Ariola, M., et al: ‘Finite-time stability of linear systems: an approach based on polyhedral Lyapunov functions’, IET Control Theory Appl., 2010, 4, (9), pp. 17671774.
    25. 25)
      • 16. Amato, F., Cosentino, C., Merola, A.: ‘Sufficient conditions for finite-time stability and stabilization of nonlinear quadratic systems’, IEEE Trans. Autom. Control, 2010, 55, (2), pp. 430434.
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