New admissibility conditions for singular linear continuous-time fractional-order systems. (English) Zbl 1355.93039
Summary: This paper deals with the admissibility problem of singular fractional-order continuous time systems. It is based on new admissibility conditions of singular fractional-order systems expressed in a set of strict Linear Matrix Inequalities (\(\mathcal{LMI}\)s). Then, a static output feedback controller is designed for the closed-loop system to be admissible. Numerical examples are given to illustrate the proposed methods.
MSC:
| 93B03 | Attainable sets, reachability |
| 93C05 | Linear systems in control theory |
| 93C15 | Control/observation systems governed by ordinary differential equations |
| 34A08 | Fractional ordinary differential equations |
Keywords:
admissibility problem; singular fractional-order continuous time systems; static output feedback controllerReferences:
| [2] | Xu, S.; Lam, J., Control and Filtering of Singular Systems (2006), Springer: Springer Berlin · Zbl 1114.93005 |
| [3] | Lewis, F. L., A survey of linear singular systems, Circuits, Systems and Signal Processing, 5, 3-36 (1986), pages · Zbl 0613.93029 |
| [4] | Luenberger, D. J., Nonlinear Descriptor Systems, J. Econ. Dyn. Control, 1, 219-242 (1979), pages |
| [5] | Wang, Z.; Shen, Y.; Zhang, X.; Wang, Q., Observer design for discrete-time descriptor systemsan LMI approach, original research article, Syst. Control Lett., 61, June (6), 683-687 (2012), pages · Zbl 1250.93038 |
| [6] | Chadli, M.; Darouach, M., Further enhancement on robust \(H_\infty\) control design for discrete-time singular systems, IEEE Trans. Autom. Control, 59, 2, 494-499 (2014), pages · Zbl 1360.93382 |
| [7] | Varga, A., On stabilization methods of descriptor systems, Syst. Control Lett., 24, 2, 133-138 (1995), pages · Zbl 0877.93092 |
| [8] | Masubuchi, I.; Kamitane, Y.; Ohara, A.; Suda, N., \(H_\infty\) control for descriptor systemsa matrix inequalities approach, Automatica, 33, 4, 669-673 (1997), pages · Zbl 0881.93024 |
| [9] | Chadli, M.; Darouach, M., Novel bounded real lemma for discrete-time descriptor systemsapplication to \(H_\infty\) control design, Automatica, 48, 2, 449-453 (2012), pages · Zbl 1260.93106 |
| [10] | Hilfer, R., Applications of Fractional Calculus in Physics (2001), World Scientific Publishing: World Scientific Publishing Singapore · Zbl 0998.26002 |
| [11] | Podlubny, I., Fractional Differential Equations (1999), Academic: Academic New-York · Zbl 0918.34010 |
| [12] | Abusaksaka, A. B.; Partington, J. R., BIBO stability of some classes of delay systems and fractional systems, Syst. Control Lett., 64, February, 43-46 (2014), Pages · Zbl 1283.93216 |
| [13] | Bagley, R.; Calico, R., Fractional order state equations for control of viscoelastically damped structures, J. Guid. Control Dyn., 14, 304-311 (1991) |
| [14] | Rossikhin, Y.; Shitikova, M., Application of fractional derivatives to the analysis of damped vibrations of viscoelastic single masse system, Acta Mechanica, 120, 125-199 (1997), pages · Zbl 0901.73030 |
| [15] | Sun, H.; Abdelwahad, A.; Onaral, B., Linear approximation of transfer function with a pole of fractional order, IEEE Trans. Autom. Control, 29, 441-444 (1984), pages · Zbl 0532.93025 |
| [16] | Ehgheta, N., On fractional calculus and fractional multipoles in electromagnetism, IEEE Trans. Antennas Propag., 44, 554-566 (1996), Pages · Zbl 0944.78506 |
| [17] | Farges, C.; Moze, M.; Sabatier, J., Pseudo-state feedback stabilization of commensurate fractional- order systems, Automatica, 46, 10, 1730-1734 (2010), Pages · Zbl 1204.93094 |
| [18] | N׳Doye, I.; Darouach, M.; Zasadzinski, M.; Radhy, N., Robust stabilisation of uncertain descriptor fractional-order systems, Automatica, 49, June (6), 1907-1913 (2013), Pages · Zbl 1360.93620 |
| [19] | Sabatier, J.; Moze, M.; Farges, C., LMI conditions for fractional order systems, Comput. Math. Appl., 59, 1594-1609 (2010), pages · Zbl 1189.34020 |
| [20] | Huang, X.; Wang, Z.; Li, Y.; Lu, J., Design of fuzzy state feedback controller for robust stabilization of uncertain fractional-order chaotic system, J. Frankl. Inst., 351, 12, 5480-5493 (2014) · Zbl 1393.93105 |
| [21] | Li, C.; Wang, J., Robust stability and stabilization of fractional order interval systems with coupling relationshipsthe \(0 < \alpha < 1\) case, J. Frankl. Inst., 349, 7, 2406-2419 (2012), pages · Zbl 1287.93063 |
| [24] | Ji, Y.; Qiu, J., Stabilization of fractional-order singular uncertain systems, ISA Trans., 56, 53-64 (2015), pages |
| [25] | Yao, Y.; Jiao, Z.; Sun, C.-Y., Sufficient and necessary condition of admissibility for fractional-order singular system, Acta Automatica Sinica, 39, 12, 2160-2164 (2013), pages |
| [26] | Boyd, S.; Elghaoui, L.; Féron, E.; Balakrishnan, V., Linear Matrix Inequality in Systems and Control Theory (1994), SIAM: SIAM Philadelphia · Zbl 0816.93004 |
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