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## International Journal of Applied Mathematics and Computer Science

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.
Słowa kluczowe
EN
Rocznik
Tom
Numer
Strony
551-560
Opis fizyczny
Daty
wydano
2012
otrzymano
2011-08-15
poprawiono
2012-03-10
Twórcy
autor
• Department of Cybernetics and Artificial Intelligence, Technical University of Košice, Letná 9/B, 042 00 Košice, Slovakia
Bibliografia
• Benzaouia, A. and Gurgat, C. (1988). Regulator problem for linear discrete-time systems with nonsymmetrical constrained control, International Journal of Control 48(6): 2441-2451.
• Boyd, D., El Ghaoui, L., Peron, E. and Balakrishnan, V. (1994). Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, PA.
• Cakmakci, M. and Ulsoy, A.G. (2009). Modular discrete optimal MIMO controller for a VCT engine, 2009 American Control Conference, St. Louis, MO, USA, pp. 1359-1364.
• Castelan, E.B. and Hennet, J.C. (1992). Eigenstructure assignment for state constrained linear continuous time systems, Automatica 28(3): 605-611.
• Debiane, L., Ivorra, B., Mohammadi, B., Nicoud, F., Ernz, A., Poinsot, T., and Pitsch, H. (2004). Temperature and pollution control in flames, Proceedings of the Summer Program 2004, Montpellier, France, pp. 1-9.
• 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.
• Gahinet, P., Nemirovski, A., Laub, A.J. and Chilali, M. (1995). LMI Control Toolbox User's Guide, The MathWorks, Natick, MA.
• Gajic, Z. and Qureshi, M.T.J. (1995). Lyapunov Matrix Equation in System Stability and Control, Academic Press, San Diego, CA.
• Hahn, H. (1992). Linear systems controlled by stabilized constraint relations. Proceedings of the 31st IEEE Conference on Decision and Control 1992, Tucson, AZ, USA, pp. 840-848.
• Herrmann, G., Turner, M.C. and Postlethwaite, I. (2007). Linear matrix inequalities in control, in M.C. Turner and D.G. Bates (Eds.), Mathematical Methods for Robust and Nonlinear Control, Springer-Verlag, Berlin, pp. 123-142.
• 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.
• Krokavec, D. and Filasová, A. (2008a). Discrete-time Systems, Elfa, Košice, (in Slovak).
• 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.
• Mason, O. and Shorten, R. (2004). On common quadratic Lyapunov functions for stable discrete-time LTI systems, IMA Journal of Applied Mathematics 69(3): 271-283.
• Nesterov, Y. and Nemirovsky, A. (1994). Interior Point Polynomial Methods in Convex Programming, Theory and Applications, SIAM, Philadelphia, PA.
• Oliveira de, M.C., Bernussou, J. and Geromel, J.C. (1999). A new discrete-time robust stability condition, Systems & Control Letters 37(4): 261-265.
• Oloomi, H. and Shafai, B. (1997). Constrained stabilization problem and transient mismatch phenomenon in singularity perturbed systems, International Journal of Control 67(2): 435-454.
• Peaucelle, D., Henrion, D., Labit, Y. and Taitz, K. (2002). User's Guide for SeDuMi Interface 1.04, LAAS-CNRS, Toulouse.
• Petersen, I.R. (2006) Minimax LQG control, International Journal of Applied Mathematics and Computer Science 16(3): 309-323.
• Skelton, R.E., Iwasaki, T. and Grigoriadis, K. (1998). A Unified Algebraic Approach to Linear Control Design, Taylor & Francis, London.
• Tarbouriech, S. and Castelan, E.B. (1995). An eigenstructure assignment approach for constrained linear continuous-time singular systems, Systems & Control Letters 24(5): 333-343.
• Veselý, V. and Rosinová, D. (2009). Robust output model predictive control design. BMI approach, International Journal of Innovative Computing, Information and Control 5(4): 1115-1123.
• Wang, Q.G. (2003). Decoupling Control, Springer-Verlag, Berlin.
• 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.
• Xie, W. (2010). An equivalent LMI representation of bounded real lemma for continous-time systems, Journal of Inequalities and Applications 2008, Article ID 672905.
• Xue, Y., Wei, Y. and Duan, G. (2006). Eigenstructure assignment for linear systems with constrained input via state feedback: A parametric approach, Proceedings of the 25th Chinese Control Conference, Harbin, China, pp. 108-113.
• Yu, T.J., Lin, C.F. and Müller, P.C. (1996). Design of LQ regulator for linear systems with algebraic-equation constraints. Proceedings of the 35th Conference on Decision and Control, Kobe, Japan, pp. 4146-4151.
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