[1]

N. K. Bose, “Applied Multidimensional System Theory,” Van Nostrand Reinhold, New York, 1982.

[2]

R. N. Bracewell, “TwoDimensional Imaging,” PrenticeHall, Englewood, 1995, pp. 505537.

[3]

C. Du, L. Xie and C. Zhang, “H_{oo} Control and Robust Stabilization of TwoDimensional Systems in Roesser Models,” Automatica, Vol. 37, No. 2, 2001, pp. 205211.
doi:10.1016/S00051098(00)001552

[4]

S. Foda and P. Agathoklis, “Control of the Metal Rolling Process: A Multidimensional System Approach,” Journal of the Franklin Institute, Vol. 329, No. 2, 1992, pp. 317332. doi:10.1016/00160032(92)90037H

[5]

T. Kaczorek, “TwoDimensional Linear Systems,” SpringerVerlag, Berlin, 1985.

[6]

W.S. Lu and A. Antoniou, “TwoDimensional Digital Filters,” Marcel Dekker, New York, 1992.

[7]

W. Marszalek, “TwoDimensional StateSpace Discrete Models for Hyperbolic Partial Differential Equations,” Applied Mathematical Modelling, Vol. 8, No. 1, 1984, pp. 1114. doi:10.1016/0307904X(84)901707

[8]

J. S.H. Tsai, J. S. Li and L.S. Shieh, “Discretized Quadratic Optimal Control for ContinuousTime TwoDimensional Systems,” IEEE Transactions on Circuits and Systems I, Vol. 49, No. 1, 2002, pp. 116125.
doi:10.1109/81.974886

[9]

M. Yamada, L. Xu and O. Saito, “2D Model Following Servo System,” Multidimensional Systems and Signal Processing, Vol. 10, No. 1, 1999, pp. 7191.
doi:10.1023/A:1008461019087

[10]

R. Yang, L. Xie and C. Zhang, “H_{2} and Mixed H_{2}/H_{oo} Control of TwoDimensional Systems in Roesser Model,” Automatica, Vol. 42, No. 9, 2006, pp. 15071514.
doi:10.1016/j.automatica.2006.04.002

[11]

R. P. Roesser, “A Discrete StateSpace Model for Linear Image Processing,” IEEE Transactions on Automatic Control, Vol. 20, No. 1, 1975, pp. 110.
doi:10.1109/TAC.1975.1100844

[12]

S. Attasi, “Modeling and Recursive Estimation for Double Indexed Sequences,” In: R. K. Mehra and D. G. Lainiotis, Eds., System Identification: Advances and Case Studies, Academic, New York, 1976, pp. 289348.
doi:10.1016/S00765392(08)608759

[13]

E. Fornasini and G. Marchesini, “StateSpace Realization Theory of TwoDimensional Filters,” IEEE Transactions on Automatic Control, Vol. 21, No. 4, 1976, pp. 484492.
doi:10.1109/TAC.1976.1101305

[14]

E. Fornasini and G. Marchesini, “Doubly Indexed Dynamical Systems: StateSpace Models and Structural Properties,” Theory of Computing Systems, Vol. 12, No. 1, 1978, pp. 5972. doi:10.1007/BF01776566

[15]

N. G. ElAgizi and M. M. Fahmy, “TwoDimensional Digital Filters with No Overflow Oscillations,” IEEE Transactions on Acoustics, Speech and Signal Processing, Vol. 27, No. 5, 1979, pp. 465469.
doi:10.1109/TASSP.1979.1163285

[16]

J. H. Lodge and M. M. Fahmy, “Stability and Overflow Oscillations in 2D StateSpace Digital Filters,” IEEE Transactions on Acoustics, Speech and Signal Processing, Vol. 29, No. 6, 1981, pp. 11611167.
doi:10.1109/TASSP.1981.1163712

[17]

B. D. O. Anderson, P. Agathoklis, E. I. Jury and M. Mansour, “Stability and the Matrix Lypunov Equation for Discrete 2Dimensional Systems,” IEEE Transactions on Circuits and Systems, Vol. 33, No. 3, 1986, pp. 261267.
doi:10.1109/TCS.1986.1085912

[18]

P. Agathoklis, E. I. Jury and M. Mansour, “The DiscreteTime Strictly BoundedReal Lemma and the Computation of Positive Definite Solutions to the 2D Lyapunov Equation,” IEEE Transactions on Circuits and Systems, Vol. 36, No. 6, 1989, pp. 830837.
doi:10.1109/31.90402

[19]

D. Liu and A. N. Michel, “Stability Analysis of State Space Realizations for TwoDimensional Filters with Overflow Nonlinearities,” IEEE Transactions on Circuits and Systems I, Vol. 41, No. 2, 1994, pp. 127137.
doi:10.1109/81.269049

[20]

H. Kar and V. Singh, “Stability Analysis of 2D State Space Digital Filters Using Lyapunov Function: A Caution,” IEEE Transactions on Signal Processing, Vol. 45, No. 10, 1997, pp. 26202621. doi:10.1109/78.640734

[21]

H. Kar and V. Singh, “Stability Analysis of 2D State Space Digital Filters with Overflow Nonlinearities,” IEEE Transactions on Circuits and Systems I, Vol. 47, No. 4, 2000, pp. 598601. doi:10.1109/81.841865

[22]

H. Kar and V. Singh, “Stability Analysis of 1D and 2D FixedPoint StateSpace Digital Filters Using Any Combination of Overflow and Quantization Nonlinearities,” IEEE Transactions on Signal Processing, Vol. 49, No. 5, 2001, pp. 10971105. doi:10.1109/78.917812

[23]

T. Bose and D. A. Trautman, “Two’s Complement Quantization in TwoDimensional StateSpace Digital Filters,” IEEE Transactions on Signal Processing, Vol. 40, No. 10, 1992, pp. 25892592. doi:10.1109/78.157299

[24]

T. Bose, “Stability of 2D StateSpace System with Overflow and Quantization,” IEEE Transactions on Circuits and Systems II, Vol. 42, No. 6, 1995, pp. 432434.
doi:10.1109/82.392319

[25]

Y. Su and A. Bhaya, “On the BoseTrautman Condition for Stability of TwoDimensional Linear Systems,” IEEE Transactions on Signal Processing, Vol. 46, No. 7, 1998, pp. 20692070. doi:10.1109/78.700987

[26]

A. Bhaya, E. Kaszkurewicz and Y. Su, “Stability of Asynchronous TwoDimensional FornasiniMarchesini Dynamical Systems,” Linear Algebra and Its Applications, Vol. 332, 2001, pp. 257263.

[27]

H. Kar and V. Singh, “Stability of 2D Systems Described by FornasiniMarchesini First Model,” IEEE Transactions on Signal Processing, Vol. 51, No. 6, 2003, pp. 16751676. doi:10.1109/TSP.2003.811237

[28]

G.D. Hu and M. Liu, “Simple Criteria for Stability of TwoDimensional Linear Systems,” IEEE Transactions on Signal Processing, Vol. 53, No. 12, 2005, pp. 47204723. doi:10.1109/TSP.2005.859265

[29]

T. Zhou, “Stability and Stability Margin for a TwoDimensional System,” IEEE Transactions on Signal Processing, Vol. 54, No. 9, 2006, pp. 34833488.
doi:10.1109/TSP.2006.879300

[30]

T. Hinamoto, “2D Lyapunov Equation and Filter Design Based on the FornasiniMarchesini Second Model,” IEEE Transactions on Circuits and Systems I, Vol. 40, No. 2, 1993, pp. 102110. doi:10.1109/81.219824

[31]

W.S. Lu, “On a Lyapunov Approach to Stability Analysis of 2D Digital Filters,” IEEE Transactions on Circuits and Systems I, Vol. 41, No. 10, 1994, pp. 665669.
doi:10.1109/81.329727

[32]

T. Ooba, “On Stability Analysis of 2D Systems Based on 2D Lyapunov Matrix Inequalities,” IEEE Transactions on Circuits and Systems I, Vol. 47, No. 8, 2000, pp. 12631265. doi:10.1109/81.873883

[33]

T. Hinamoto, “Stability of 2D Discrete Systems Described by the FornasiniMarchesini Second Model,” IEEE Transactions on Circuits and Systems I, Vol. 44, No. 3, 1997, pp. 254257.
doi:10.1109/81.557373

[34]

D. Liu, “Lyapunov Stability of TwoDimensional Digital Filters with Overflow Nonlinearities,” IEEE Transactions on Circuits and Systems I, Vol. 45, No. 5, 1998, pp. 574577. doi:10.1109/81.668870

[35]

H. Kar and V. Singh, “An Improved Criterion for the Asymptotic Stability of 2D Digital Filters Described by the FornasiniMarchesini Second Model Using Saturation Arithmetic,” IEEE Transactions on Circuits and Systems I, Vol. 46, No. 11, 1999, pp. 14121413.
doi:10.1109/81.802847

[36]

H. Kar and V. Singh, “Stability Analysis of 2D Digital Filters Described by the FornasiniMarchesini Second Model Using Overflow Nonlinearities,” IEEE Transactions on Circuits and Systems I, Vol. 48, 2001, pp. 612617.

[37]

C. Du, L. Xie and Y. C. Soh, “H_{oo}Filtering of 2D Discrete Systems,” IEEE Transactions on Signal Processing, Vol. 48, No. 6, 2000, pp. 17601768.
doi:10.1109/78.845933

[38]

H. Kar and V. Singh, “Robust Stability of 2D Discrete Systems Described by the FornasiniMarchesini Second Model Employing Quantization/Overflow Nonlinearities,” IEEE Transactions on Circuits and Systems II, Vol. 51, No. 11, 2004, pp. 598602.
doi:10.1109/TCSII.2004.836880

[39]

C. Du and L. Xie, “Stability Analysis and Stabilization of Uncertain TwoDimensional Discrete Systems: An LMI Approach,” IEEE Transactions on Circuits and Systems I, Vol. 46, No. 11, 1999, pp. 13711374.
doi:10.1109/81.802835

[40]

C. Du and L. Xie, “LMI Approach to Output Feedback Stabilization of 2D Discrete Systems,” International Journal of Control, Vol. 72, No. 2, 1999, pp. 97106.
doi:10.1080/002071799221262

[41]

T. Bose, M. Q. Chen, K. S. Joo and G. F. Xu, “Stability of TwoDimensional Discrete Systems with Periodic Coefficients,” IEEE Transactions on Circuits and Systems II, Vol. 45, No. 7, 1998, pp. 839847.
doi:10.1109/82.700930

[42]

X. Guan, C. Long and G. Duan, “Robust Optimal Guaranteed Cost Control for 2D Discrete Systems,” IET Control Theory & Applications, Vol. 148, 2001, pp. 355361.

[43]

A. Dhawan and H. Kar, “LMIBased Criterion for the Robust Guaranteed Cost Control of 2D Systems Described by the FornasiniMarchesini Second Model,” Signal Processing, Vol. 87, No. 3, 2007, pp. 479488.
doi:10.1016/j.sigpro.2006.06.002

[44]

A. Dhawan and H. Kar, “Optimal Guaranteed Cost Control of 2D Discrete Uncertain Systems: An LMI Approach,” Signal Processing, Vol. 87, No. 12, 2007, pp. 30753085. doi:10.1016/j.sigpro.2007.06.001

[45]

S. S. L. Chang and T. K. C. Peng, “Adaptive Guaranteed Cost Control Systems with Uncertain Parameters,” IEEE Transactions on Automatic Control, Vol. 17, No. 4, 1972, pp. 474483. doi:10.1109/TAC.1972.1100037

[46]

I. R. Petersen and D. C. Mcfarlane, “Optimal Guaranteed Cost Control and Filtering for Uncertain Linear Systems,” IEEE Transactions on Automatic Control, Vol. 39, No. 9, 1994, pp. 19711977. doi:10.1109/9.317138

[47]

I. R Petersen, D. C. Mcfarlane and M. A. Rotea, “Optimal Guaranteed Cost Control of DiscreteTime Uncertain Linear Systems,” International Journal of Robust and Nonlinear Control, Vol. 8, No. 8, 1998, pp. 649657.
doi:10.1002/(SICI)10991239(19980715)8:8<649::AIDRNC334>3.0.CO;26

[48]

M. S. Mahmoud and L. Xie, “Guaranteed Cost Control of Uncertain Discrete Systems with Delays,” International Journal of Control, Vol. 73, No. 2, 2000, pp. 105114.
doi:10.1080/002071700219812

[49]

H. Mukaidani, “An LMI Approach to Guaranteed Cost Control for Uncertain Delay Systems,” IEEE Transactions on Circuits and Systems I, Vol. 50, No. 6, 2003, pp. 795800. doi:10.1109/TCSI.2003.812620

[50]

X. Nian and J. Feng, “Guaranteed Cost Control of a Linear Uncertain System with Multiple TimeVarying Delays: An LMI Approach,” IET Control Theory & Applications, Vol. 150, 2003, pp. 1722.

[51]

L. Xie and Y. C. Soh, “Guaranteed CostControl of Uncertain DiscreteTime Systems,” Control Theory and Advanced Technology, Vol. 10, 1995, pp. 12351251.

[52]

S. Boyd, L. El Ghaoui, E. Feron and V. Balakrishnan, “Linear Matrix Inequalities in System and Control Theory,” SIAM, Philadelphia, 1994.
doi:10.1137/1.9781611970777

[53]

P. Gahinet, A. Nemirovski, A. J. Laub and M. Chilali, “LMI Control Toolbox—for Use with Matlab,” The MATH Works Inc., Natick, 1995.

[54]

V. Balakrishnan and E. Feron, “Linear Matrix Inequalities in Control Theory and Applications,” International Journal of Robust Nonlinear Control, Special Issue, 1996, pp. 8961099.

[55]

L. El Ghaoui and S. I. Niculescu, “Advances in Linear Matrix Inequality Methods in Control, Advances in Design and Control,” SIAM, Philadelphia, 2000.

[56]

T. Iwasaki, “LMI and Control,” Shokodo, Japan, 1997.

[57]

Y. Nesterov and A. Nemirovskii, “InteriorPoint Polynomial Algorithms in Convex Programing,” SIAM, Philadelphia, 1994.

[58]

L. Vandenberghe and V. Balakrishnan, “Algorithms and Software for LMI Problems in Control,” IEEE Control Systems, Vol. 17, No. 5, 1997, pp. 8995.
doi:10.1109/37.621480

[59]

S. Xu, J. Lam, Z. Lin and K. Galkowski, “Positive Real Control for Uncertain TwoDimensional Systems,” IEEE Transactions on Circuits and Systems I, Vol. 49, No. 11, 2002, pp. 16591666. doi:10.1109/TCSI.2002.804531

[60]

P. P. Khargonekar, I. R. Petersen and K. Zhou, “Robust Stabilization of Uncertain Linear Systems: Quadratic Stability and H_{oo} Control Theory,” IEEE Transactions on Automatic Control, Vol. 35, 1991, pp. 356361.

[61]

L. Xie, M. Fu and C. E. De Souza, “H_{oo} Control and Quadratic Stabilization of Systems with Parameter Uncertainty via Output Feedback,” IEEE Transactions on Automatic Control, Vol. 37, No. 8, 1992, pp. 12531256.
doi:10.1109/9.151120

[62]

F. Yang and Y. S. Hung, “Robust Mixed H_{2}/H_{oo} Filtering with Regional Pole Assignment for Uncertain DiscreteTime Systems,” IEEE Transactions on Circuits and Systems I, Vol. 49, No. 8, 2002, pp. 12361241.
doi:10.1109/TCSI.2002.801267

[63]

M. S. Mahmoud, “Robust Control and Filtering for TimeDelay Systems,” MarcelDekker, New York, 2000.
