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Robust Suboptimal Guaranteed Cost Control for 2-D Discrete Systems Described by Fornasini-Marchesini First Model
Electronics and Communication Engineering Department, Motilal Nehru National Institute of Technology, Allahabad, India.
Electronics and Communication Engineering Department, Motilal Nehru National Institute of Technology, Allahabad, India.
- 1 Electronics and Communication Engineering Department, Motilal Nehru National Institute of Technology, Allahabad, India.
- 2 Electronics and Communication Engineering Department, Motilal Nehru National Institute of Technology, Allahabad, India.
Journal of Signal and Information Processing·Volume 03 (2012)·Pages 252–258·Published 30 May 2012·DOI10.4236/jsip.2012.32034
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Abstract
This paper considers the guaranteed cost control problem for a class of two-dimensional (2-D) uncertain discrete systems described by the Fornasini-Marchesini (FM) first model with norm-bounded uncertainties. New linear matrix inequality (LMI) based characterizations are presented for the existence of static-state feedback guaranteed cost controller which guarantees not only the asymptotic stability of closed loop systems, but also an adequate performance bound over all the admissible parameter uncertainties. Moreover, a convex optimization problem is formulated to select the suboptimal guaranteed cost controller which minimizes the upper bound of the closed-loop cost function.
KeywordsGuaranteed Cost ControlLinear Matrix InequalityLyapunov MethodsRobust Stability2-D Discrete SystemsUncertain Systems
- A. T. Kaczorek, “Two-Dimensional Linear Systems,” Springer-Verlag: Berlin, 1985.
- R. N. Bracewell, “Two-Dimensional Imaging,” Prentice-Hall Signal Processing Series, Prentice-Hall, Englewood Cliffs, 1995.
- W.-S. Lu and A. Antoniou, “Two-Dimensional Digital Filters,” Marcel Dekker, New York, 1992.
- N. K. Bose, “Applied Multidimensional System Theory,” Van Nostrand Reinhold, New York, 1982.
- W. Marszalek, “Two-Dimensional State-Space Discrete Models for Hyperbolic Partial Differential Equations,” Applied Mathematical Modelling, Vol. 8, No. 1, 1984, pp. 11-14. doi:10.1016/0307-904X(84)90170-7
- C. Du, L. Xie and C. Zhang, “ H oo Control and Robust Stabilization of Two-Dimensional Systems in Roesser Models,” Automatica, Vol. 37, No. 2, 2001, pp. 205-211. doi:10.1016/S0005-1098(00)00155-2
- J. S.-H. Tsai, J. S. Li and L.-S. Shieh, “Discretized Quadratic Optimal Control for Continuous-Time Two-Dimensional Systems,” IEEE Transactions on Circuits and Systems I, Vol. 49, No. 1, 2002, pp. 116-125.
- R. Yang, L. Xie and C. Zhang, “H2 and Mixed H 2 / H oo Control of Two-Dimensional Systems in Roesser Model,” Automatica, Vol. 42, No. 9, 2006, pp. 1507-1514. doi:10.1016/j.automatica.2006.04.002
- E. Fornasini and G. Marchesini, “State-Space Realization Theory of Two Dimensional Filters,” IEEE Transactions on Automatic Control, Vol. 21, No. 4, 1976, pp. 484-492. doi:10.1109/TAC.1976.1101305
- G.-D. Hu and M. Liu, “Simple Criteria for Stability of Two-Dimensional Linear Systems,” IEEE Transactions on Signal Processing, Vol. 53, No. 12, 2005, pp. 4720-4723. doi:10.1109/TSP.2005.859265
- T. Bose and D. A. Trautman, “Two’s Complement Quantization in Two-Dimensional State-Space Digital Filters,” IEEE Transactions on Signal Processing, Vol. 40, No. 10, 1992, pp. 2589-2592. doi:10.1109/78.157299
- Y. Su and A. Bhaya, “On the Bose-Trautman Condition for Stability of Two-Dimensional Linear Systems,” IEEE Transactions on Signal Processing, Vol. 46, No. 7, 1998, pp. 2069-2070. doi:10.1109/78.700987
- T. Bose, “Stability of 2-D State-Space System with Over-flow and Quantization,” IEEE Transactions on Circuits and Systems II, Vol. 42, No. 6, 1995, pp. 432-434. doi:10.1109/82.392319
- H. Kar and V. Singh, “Stability of 2-D Systems Described by Fornasini-Marchesini First Model,” IEEE Transactions on Signal Processing, Vol. 51, No. 6, 2003, pp. 1675-1676. doi:10.1109/TSP.2003.811237