Article
Full entry |
PDF
(0.8 MB)
Feedback
PDF
(0.8 MB)
Feedback
Keywords:
differential LMIs; finite time stability; guaranteed cost control; robust control; state feedback control
differential LMIs; finite time stability; guaranteed cost control; robust control; state feedback control
Summary:
This paper deals with the design of a robust state feedback control law for a class of uncertain linear time varying systems. Uncertainties are assumed to be time varying, in one-block norm bounded form. The proposed state feedback control law guarantees finite time stability and satisfies a given bound for an integral quadratic cost function. The contribution of this paper is to provide a sufficient condition in terms of differential linear matrix inequalities for the existence and the construction of the proposed robust control law. In particular, the construction of the feedback control law is brought back to a feasibility problem which can be solved inside the convex optimization framework. The effectiveness of the proposed approach is shown by means of the results obtained on a numerical and a physical example.
References:
[1] Amato, F., Ambrosino, R., Ariola, M., Cosentino, C., Tommasi, G. De: Finite-Time Stability and Control. Springer Verlag, 2014. MR 3157178
[2] Amato, F., Ambrosino, R., Ariola, M., Tommasi, G. De: Robust finite-time stability of impulsive dynamical linear systems subject to norm-bounded uncertainties. Int. J. Robust Nonlinear Control 21 (2011), 1080-1092. DOI 10.1002/rnc.1620 | MR 2839840
[3] Amato, F., Ariola, M., Cosentino, C.: Finite-time stability of linear time-varying systems: Analysis and controller design. IEEE Trans. Automat. Control 55 (2010), 4, 1003-1008. DOI 10.1109/tac.2010.2041680 | MR 2654445
[4] Amato, F., Ariola, M., Cosentino, C.: Robust finite-time stabilisation of uncertain linear systems. Int. J. Control 84 (2011), 12, 2117-2127. DOI 10.1080/00207179.2011.633230 | MR 2869612
[5] Amato, F., Ariola, M., Dorato, P.: Finite-time control of linear systems subject to parametric uncertanties and disturbances. Automatica 37 (2001), 1459-1463. DOI 10.1016/s0005-1098(01)00087-5
[6] Amato, F., Cosentino, C., Tommasi, G. De, Pironti, A.: New conditions for the finite-time stability of stochastic linear time-varying systems. In: Proc. European Control Conference, (2015), pp. 1213-1218. DOI 10.1109/ecc.2015.7330706
[7] Amato, F., Cosentino, C., Tommasi, G. De, Pironti, A.: The mixed robust $H_\infty$/FTS control problem. Asian J. Control 18 (2016), 3, 828-841. DOI 10.1002/asjc.1196 | MR 3502465
[8] Amato, F., Tommasi, G. De, Pironti, A.: Necessary and sufficient conditions for finite-time stability of impulsive dynamical linear systems. Automatica 49 (2013), 8, 2546-2550. DOI 10.1016/j.automatica.2013.04.004 | MR 3072649
[9] Amato, F., Tommasi, G. De, Mele, A., Pironti, A.: New conditions for annular finite-time stability of linear systems. In: IEEE 55th Conference on Decision and Control (2016), pp. 4925-4930. DOI 10.1109/cdc.2016.7799022
[10] Ambrosino, R., Calabrese, F., Cosentino, C., Tommasi, G. De: Sufficient conditions for finite-time stability of impulsive dynamical systems. IEEE Trans. Automat. Control 54 (2009), 4, 861-865. DOI 10.1109/tac.2008.2010965 | MR 2514824
[11] Anderson, B. D .O., Moore, J. B.: Optimal Control: Linear Quadratic Methods. Englewood Cliffs, Prentice-Hall, NJ 1989. MR 0335000
[12] Chen, J., Li, Q., Liu, C.: Guaranteed cost control of uncertain impulsive switched systems with nonlinear disturbances. In: UKACC International Conference on Control, (2014). DOI 10.1109/control.2014.6915131
[13] Corless, M.: Variable Structure and Lyapunov Control, chapter Robust stability analysis and controller design with quadratic Lyapunov functions. Springer Verlag, (A. S. I. Zinober, ed.), London (1994). DOI 10.1007/bfb0033675 | MR 1257919
[14] Dorato, P.: Short time stability in linear time-varying systems. In: Proc. IRE International Convention Record Part 4, (1961), pp. 83-87.
[15] Golestani, M., Mobayen, S., Tchier, F.: Adaptive finite-time tracking control of uncertain non-linear n-order systems with unmatched uncertainties. IET Control Theory Appl. 10 (2016), 1675-1683. DOI 10.1049/iet-cta.2016.0163 | MR 3585276
[16] Haddad, W. M., L'Afflitto, A.: Finite-time stabilization and optimal feedback control. IEEE Trans. Automat. Control 61 (2016), 4, 1069-1074. DOI 10.1109/tac.2015.2454891 | MR 3483539
[17] Li, L., Yan, G.: Sufficient optimality conditions for impulsive and switching optimal control problems. In: Proc. 34th Chinese Control Conference, (2015). DOI 10.1109/chicc.2015.7260012
[18] Mastellone, S., Dorato, P., Abdallah, C. T.: Finite-time stability of discrete-time nonlinear systems: analysis and design. In: Proc. IEEE Conference on Decision and Control, (2004), pp. 2572-2577. DOI 10.1109/cdc.2004.1428845
[19] Mobayen, S., Tchier, F.: A new LMI-based robust finite-time sliding mode control strategy for a class of uncertain nonlinear systems. Kybernetika 51 (2015), 1035-1048. DOI 10.14736/kyb-2015-6-1035 | MR 3453684
[20] Moheimani, S. O. R., Petersen, I. R.: Optimal guaranteed cost control of uncertain systems via static and dynamic output feedback. Automatica 32 (1996), 4, 575-579. DOI 10.1016/0005-1098(95)00178-6 | MR 1386704
[21] Petersen, I. R., McFarlane, D. C.: Optimal guaranteed cost control of uncertain linear systems. In: American Control Conference (1992), pp. 2929-2930. DOI 10.23919/acc.1992.4792682 | MR 1293449
[22] Petersen, I. R., McFarlane, D. C., Rotea, M. A.: Optimal guaranteed cost control of discrete-time uncertain linear systems. Int. J. Robust Nonlinear Control 8 (1998), 7, 649-657. DOI 10.1002/(sici)1099-1239(19980715)8:8<649::aid-rnc334>3.3.co;2-y | MR 1632206
[23] Qayyum, A.: Finite time output regulation of sampled data linear systems through impulsive observer. In: Proc. SICE International Symposium on Control Systems (2017), pp. 62-66.
[24] Qayyum, A., Tommasi, G. De: Finite-time state estimation of sampled output impulsive dynamical linear system. In: Proc. 24th Mediterranean Conference on Control and Automation (2016), pp. 154-158. DOI 10.1109/MED.2016.7535975
[25] Qayyum, A., Malik, M. B., Tommasi, G. De, Pironti, A.: Finite time estimation of a linear system based on sampled measurement through impulsive observer. In: Proc. 28th Chinese Control and Decision Conference (2016), pp. 978-981. DOI 10.1109/CCDC.2016.7531125
[26] Qayyum, A., Pironti, A.: Finite time stability with guaranteed cost control for linear systems. In: Proc. 21st International Conference on System Theory, Control and Computing (2017). DOI 10.1109/ICSTCC.2017.8107124
[27] Qayyum, A., Salman, M., Malik, M. B.: Receding horizon observer for linear time-varying systems. In: Trans. Inst. Measurement and Control (2018). DOI 10.1177/0142331218805153
[28] Ren, J., Zhang, Q.: Robust normalization and guaranteed cost control for a class of uncertain descriptor systems. Automatica 48 (2012), 5, 1693-1697. DOI 10.1016/j.automatica.2012.05.038 | MR 2950418
[29] Vaseghi, B., Pourmina, M. A., Mobayen, S.: Finite-time chaos synchronization and its application in wireless sensor networks. In: Trans. Inst. Measurement and Control (2017). DOI 10.1177/0142331217731617
[30] Xu, H. L., Teo, K. L., Liu, X. Z.: Robust stability analysis of guaranteed cost control for impulsive switched systems. IEEE Trans. Automat. Contrpl 38 (2008), 5, 1419-1422. DOI 10.1109/tsmcb.2008.925747
[31] Yan, Z., Zhang, G., Zhang, W.: Finite-time stability and stabilization of linear ito stochastic systems with state and control dependent noise. Asian J. Control 15 (2013), 270-281. DOI 10.1002/asjc.531 | MR 3015775
[32] Yan, Z., Zhang, W., Zhang, G.: Finite-time stability and stabilization of it's stochastic systems with markovian switching: Mode-dependent parameter approach. IEEE Trans. Automat. Control 60 (2015), 9, 2428-2433. DOI 10.1109/tac.2014.2382992 | MR 3393133
[33] Zhao, S., Sun, J., Liu, L.: Finite-time stability of linear time-varying singular systems with impulsive effects. Int. J. Control 81 (2008), 11, 1824-1829. DOI 10.1080/00207170801898893 | MR 2462577
Search
Partner of
