A new D-stability area for linear discrete-time systems

• Autorzy: Krokavec Dušan , Filasová Anna

Identyfikatory

DOI

10.24425/acs.2018.125488

• Języki publikacji: EN

Abstrakty

EN

The paper addresses the problem of constrained pole placement in discrete-time linear systems. The design conditions are outlined in terms of linear matrix in equalities for the D-stable ellipse region in the complex Z plain. In addition, it is demonstrated that the D-stable circle region formulation is the special case of by this way formulated and solved pole placement problem. The proposed principle is enhanced for discrete-time linear systems with polytopic uncertainties.

Słowa kluczowe

EN

discrete-time linear systems; state control; pole placement onstraints; D-stability region; linear matrix inequalities; polytopic uncertainties

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2019
• Tom: Vol. 29, No. 1
• Strony: 5--23
• Opis fizyczny: Bibliogr. 21 poz., wykr., wzory

Twórcy

autor

Krokavec Dušan

• Technical University of Košice, Faculty of Electrical Engineering and Informatics, Department of Cybernetics and Artificial Intelligence, Letná 9, 042 00 Košice, Slovakia

autor

Filasová Anna

• Technical University of Košice, Faculty of Electrical Engineering and Informatics, Department of Cybernetics and Artificial Intelligence, Letná 9, 042 00 Košice, Slovakia

Bibliografia

• [1] J. Ackerman: Robust Control. Systems with Uncertain Physical Parameters, Springer–Verlag, Berlin, 1993.
• [2] W. Assawinchaichote, S. K. Nguang, P. Shi, and E. K. Boukas: H∞ fuzzy state-feedback control design for nonlinear systems with D-stability constraints. An LMI approach, Mathematics and Computers in Simulation, 78(4) (2008), 514–531.
• [3] J. Bai, H. Su, J. Wang, and B. Shi: On pole placement in LMI region for descriptor linear systems, Int. J. of Innovative Computing, Information and Control, 8(4) (2012), 2613–2624.
• [4] M. Chilali and P. Gahinet: H∞ design with pole placement constraints. An LMI Approch, Proc. 33rd Conference on Decision and Control, Lake Buena Vista, FL, USA (1994), 553–558.
• [5] M. Chilali and P. Gahinet: H∞ design with pole placement constraints. An LMI Approch, IEEE Tran. Automatic Control, 41(3) (1996), 358–361.
• [6] K. Furuta and S. B. Kim: Pole assignment in a specified disk, IEEE Tran. Automatic Control, 32(5) (1987), 423–427.
• [7] L. Gao and W. Chen: D-admissibility conditions of singular systems, Int. J. of Control, Automation, and Systems, 5(1) (2007), 86–92.
• [8] W. M. Haddad and D. S. Bernstein: Controller design with regional pole constraints, IEEE Tran. Automatic Control, 37(1) (1992), 54–69.
• [9] W. M. Haddad and V. Chellaboina: Nonlinear Dynamical Systems and Control. A Lyapunov-Based Approach, Princeton University Press, Princeton, 2008.
• [10] Z. X. Han, G. Feng, B. L.Walcott, and Y. M. Zhang: H∞ controller design of fuzzy dynamic systems with pole placement constraints, Proc. 2000 American Control Conference. Vol. 3, Chicago, IL, USA, (2000), 1939–1943.
• [11] S. K. Hong and R. Langari: An LMI-based H∞ fuzzy control system design with TS framework, Information Sciences, 123(3-4) (2000), 163–179.
• [12] S. K. Hong and Y. Nam: Stable fuzzy control system design with pole placement constraint. An LMI approach, Computers in Industry, 51(1) (2003), 1–11.
• [13] Y. Ishihara and Y. Chida: Extended H∞ control with pole placement constraints via LMI approach and its application, Proc. 16th IFAC World Congress, Prague, Czech Republic (2005), 959–959.
• [14] J. Joh, R. Langari, E. T. Jeung, andW.J. Chung: A new design method for continuous Takagi-Sugeno fuzzy controllerwith pole placement constraints. An LMI approach, Proc. IEEE Int. Conf. on Systems,Man, and Cybernetics, Orlando, FL, USA (1997), 2969–2974.
• [15] M. Kchaou, M. Souissi, and A. Toumi: Robust H∞ output feedback control with pole placement constraints for uncertain discrete-time fuzzy systems, Soft Computing, 17(5) (2013), 769–781.
• [16] D. Krokavec and A. Filasová: Equivalent representations of bounded real lemma, Proc. 18th Int. Conf. on Process Control PC’2011, Tatranská Lomnica, Slovakia (2011), 106–110.
• [17] D. Krokavec and A. Filasová: On pole placement LMI constraints in control design for linear discrete-time systems, Proc. 19th Int. Conf. on Process Control PC’2013, Štrbske Pleso, Slovakia (2013), 69–74.
• [18] D. Krokavec and A. Filasová: LMI constraints on system eigen values placement in dynamic output control design, Proc. 2015 IEEE Int. Conf. on Control Applications CCA 2015, Sydney, Australia (2015), 1749–1754.
• [19] D. Krokavec, A. Filasová, and P. Liščinský: D-stable condition for cascade reconfiguration control design, Proc. 3rd Int. Conf. on Control, Decision and Information Technologies CoDiT’16, St. Paul`s Bay, Malta (2016), 633–638.
• [20] D. Peaucelle, D. Arzelier, O. Bachelier, and J. Bernussou: A new robust D-stability condition for real convex polytopic uncertainty. Systems & Control Letters, 40(1) (2000), 21–30.
• [21] D. Peaucelle, D. Henrion, Y. Labit, and K. Taitz: User’s Guide for SeDuMi Interface 1.04. LAAS-CNRS, Toulouse, 2002.

Uwagi

EN

1. The work presented in this paper was supported by VEGA, the Grant Agency of the Ministry of ducation and the Academy of Science of Slovak Republic, under Grant No. 1/0608/17. This support is very gratefully acknowledged.

PL

2. Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).