Abstract
Uncertainties are one of the main causes for instabilities and poor performance in feedback systems. Thus, robust stability is an important issue for any control design, so this chapter incorporates uncertainty into the control methodologies for two-dimensional systems studied in Chap. 2.
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A. Hmamed, M. Alfidi, A. Benzaouia, F. Tadeo, LMI conditions for robust stability of 2-D linear discrete-time systems. Math. Probl. Eng. 2008, Article ID 356124, 11 pp. (2008)
S. Boyd, L. El Ghaoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory (SIAM Studies in Applied Mathematics, Philadelphia, 1994)
B.R. Barmish, Necessary and sufficient conditions for quadratic stabilizability of an uncertain system. J. Optim. Theory Appl. 46(4), 399–408 (1985)
J. Bernussou, P.L.D. Peres, J.C. Geromel, A linear programming oriented procedure for quadratic stabilization of uncertain systems. Syst. Control Lett. 13(1), 65–72 (1989)
H.R. Karimi, Robust stabilization with \(H_\infty \) performance for a class of linear parameter-dependent systems. Math. Probl. Eng. 2006, Article ID 59867, 15 pp. (2006)
Z. Duan, J. Zhang, C. Zhang, E. Mosca, Robust \(H_{2}\) and \(H_{\infty }\) filtering for uncertain linear systems. Automatica 42(11), 1919–1926 (2006)
M.C. De Oliveira, J.C. Geromel, L.H. Su, LMI characterization of structural and robust stability: the discrete-time case. Linear Algebra Appl. 296(1–3), 27–38 (1999)
V.J.S. Leite, P.L.D. Peres, An improved LMI condition for robust D-stability of uncertain polytopic systems. IEEE Trans. Autom. Control 48(3), 500–504 (2003)
D.C.W. Ramos, P.L.D. Peres, A less conservative LMI condition for the robust stability of discrete-time uncertain systems. Syst. Control Lett. 43(5), 371–378 (2001)
A. Rantzer, M. Johansson, Piecewise linear quadratic optimal control. IEEE Trans. Autom. Control 45(4), 629–637 (2000)
L. Xie, C. Du, C. Zhang, Y.C. Soh, \(H_{2}/H_{\infty }\) deconvolution filtering of 2-D digital systems. IEEE Trans. Signal Process. 50(9), 2319–2332 (2002)
D. Peaucelle, D. Arzelier, O. Bachelier, J. Bernussou, A new robust D-stability condition for real convex polytopic uncertainty. Syst. Control Lett. 40(1), 21–30 (2000)
A. Hmamed, M. Alfidi, A. Benzaouia, F. Tadeo, Robust stabilization under linear fractional parametric uncertainties of two-dimensional system with Roesser models. Int. J. Sci. Tech. Autom. Control Comput. Eng., Spec. Issue, 1(1), 336–348 (2007)
A. Hmamed, M. Alfidi, A. Benzaouia, F. Tadeo, Robust stabilization of two-dimensional systems with Roesser models under linear fractional parametric uncertainties, in Conference on Systems and Control, Marrakesh, Morocco, 16–18 May 2007
M. Alfidi, Analyse et synthse robustes des systmes linaires bidimensionnels. Ph.D. thesis, University Mohamed Ben Abdallah, Fès, Morocco (2009)
E. Fornasini, G. Marchesini, Doubly-indexed dynamical systems: state-space models and structural properties. Math. Syst. Theory 12(1), 59–72 (1978)
T. Hinamoto, 2-D Lyapunov equation and filter design based on Fornasini–Marchesini second model. IEEE Trans. Circuits Syst. I: Fundam. Theory Appl. 40(2), 102–110 (1993)
S.W. Kau, Y.S. Liu, L. Hong, C.H. Lee, C.H. Fang, L. Lee, A new LMI condition for robust stability of discrete-time uncertain systems. Syst. Control Lett. 54(12), 1195–1203 (2005)
L. Guo, \(H_{\infty }\) output feedback control for delay systems with nonlinear and parametric uncertainties. IEE Proc. Control Theory Appl. 149(3), 226–236 (2002)
S. Xu, J. Lam, Y. Zou, Z. Lin, W. Paszke, Robust \(H_{\infty }\) filtering for uncertain 2-D continuous systems. IEEE Trans. Signal Process. 53(5), 1731–1738 (2005)
S.S. Zou, J. Lam, Robust stabilization of delayed singular systems with linear fractional parametric uncertainties. Circuits Syst. Signal Process. 22(6), 579–588 (2003)
C. Du, L. Xie, Stability analysis and stabilization of uncertain two-dimensional discrete systems: an LMI approach. IEEE Trans. Circuits Syst. I 46(11), 1371–1374 (1999)
A. Dhawan, H. Kar, LMI-based criterion for the robust guaranteed cost control of 2-D systems described by the Fornasini–Marchesini second model. Signal Process. 87(12), 479–488 (2007)
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Benzaouia, A., Hmamed, A., Tadeo, F. (2016). Robust Stabilization of Two-Dimensional Uncertain Systems. In: Two-Dimensional Systems. Studies in Systems, Decision and Control, vol 28. Springer, Cham. https://doi.org/10.1007/978-3-319-20116-0_5
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DOI: https://doi.org/10.1007/978-3-319-20116-0_5
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