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2012 | 22 | 3 | 551-560
Tytuł artykułu

$H_∞$ control of discrete-time linear systems constrained in state by equality constraints

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, stabilizing problems in control design are addressed for linear discrete-time systems, reflecting equality constraints tying together some state variables. Based on an enhanced representation of the bounded real lemma for discretetime systems, the existence of a state feedback control for such conditioned stabilization is proven, and an LMI-based design procedure is provided. The control law gain computation method used circumvents generally an ill-conditioned singular design task. The principle, when compared with previously published results, indicates that the proposed method outperforms the existing approaches, guarantees feasibility, and improves the steady-state accuracy of the control. Furthermore, better performance is achieved with essentially reduced design effort. The approach is illustrated on simulation examples, where the validity of the proposed method is demonstrated using one state equality constraint.
Rocznik
Tom
22
Numer
3
Strony
551-560
Opis fizyczny
Daty
wydano
2012
otrzymano
2011-08-15
poprawiono
2012-03-10
Twórcy
  • Department of Cybernetics and Artificial Intelligence, Technical University of Košice, Letná 9/B, 042 00 Košice, Slovakia
Bibliografia
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  • Dórea, C.E.T. and Milani, B.E.A. (1995). Design of L-Q regulators for state constrained continuous-time systems, IEEE Transactions on Automatic Control AC-40(3): 544-548.
  • Filasová, A. and Krokavec, D. (2010). Observer state feedback control of discrete-time systems with state equality constraints, Archives of Control Sciences 20(3): 253-266.
  • Filasová, A. and Krokavec, D. (2011). Constrained $H_∞$ control of discrete-time systems. Proceedings of the 15th WSEAS International Conference on Systems, 2011, Corfu, Greece, pp. 153-158.
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  • Kaczorek, T. (2002). Externally and internally positive singular discrete-time linear systems, International Journal of Applied Mathematics and Computer Science 12(2): 197-202.
  • Ko, S. and Bitmead, R.R. (2007a). Optimal control for linear systems with state equality constraints, Automatica 43(9): 1573-1582.
  • Ko, S. and Bitmead, R.R. (2007b). State estimation for linear systems with state equality constraints, Automatica 43(9): 1363-1368.
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  • Krokavec, D. and Filasová, A. (2008b). Constrained control of discrete-time stochastic systems, Proceedings of the 17th IFAC World Congress, Seoul, Korea, pp. 15315-15320.
  • Krokavec, D. and Filasová, A. (2008c). Performance of reconfiguration structures based on the constrained control, Proceedings of the 17th IFAC World Congress, Seoul, Korea, pp. 1243-1248.
  • Krokavec, D. and Filasová, A. (2009). Control reconfiguration based on the constrained LQ control algorithms, Preprints of the 7th IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes, SAFEPROCESS 2009, Barcelona, Spain, pp. 686-691.
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  • Wu, A.I. and Duan, G.R. (2006). Enhanced LMI representations for H₂ performance of polytopic uncertain systems: Continuous-time case, International Journal of Automation and Computing 3(3): 304-308.
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Bibliografia
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