Non-Fragile Controller Design for 2-D Discrete Uncertain Systems Described by the Roesser Model

Amit Dhawan^{*}

Show more

References

[1] T. Kaczorek, “Two-Dimensional Linear Systems,” Springer-Verlag, Berlin, 1985.

[2]
R. N. Bracewell, “Two-Dimensional Imaging,” Prentice-Hall Signal Processing Series, Prentice-Hall, Englewood Cliffs, 1995.

[3]
W.-S. Lu and A. Antoniou, “Two-Dimensional Digital Filters,” Marcel Dekker, New York, 1992.

[4]
N. K. Bose, “Applied Multidimensional System Theory,” Van Nostrand Reinhold, New York, 1982.

[5]
R. P. Roesser, “A Discrete State-Space Model for Linear Image Processing,” IEEE Transactions on Automatic Control, Vol. 20, No. 1, 1975, pp. 1-10.

[6]
B. D. O. Anderson, P. Agathoklis, E. I. Jury and M. Mansour, “Stability and the Matrix Lypunov Equation for Discrete 2-Dimensional Systems,” IEEE Transactions on Circuits and Systems, Vol. 33, 1986, pp. 261-267.
doi:10.1109/TCS.1986.1085912

[7] H. Kar and V. Singh, “Stability Analysis of 2-D State-Space Digital Filters Using Lyapunov Function: A Caution,” IEEE Transactions on Signal Process, Vol. 45, No. 10, 1997, pp. 2620-2621. doi:10.1109/78.640734

[8]
H. Kar and V. Singh, “Stability Analysis of 1-D and 2-D Fixed-Point State-Space Digital Filters Using Any Combination of Overflow and Quantization Nonlinearities,” IEEE Transactions on Signal Process, Vol. 49, 2001, pp. 1097-1105. doi:10.1109/78.917812

[9]
D. Liu and A. N. Michel, “Stability Analysis of State-Space Realizations for Two-Dimensional Filters with Over-flow Nonlinearities,” IEEE Transactions on Circuits and Systems I, Vol. 41, No. 2, 1994, pp. 127-137.
doi:10.1109/81.269049

[10]
H. Kar and V. Singh, “Stability Analysis of 2-D State-Space Digital Filters with Overflow Nonlinearities,” IEEE Transactions on Circuits and Systems I, Vol. 47, No. 4, 2000, pp. 598-601. doi:10.1109/81.841865

[11]
V. Singh, “New LMI Condition for the Nonexistence of Overflow Oscillations in 2-D State-Space Digital Filters Using Saturation Arithmetic,” Digital Signal Process, Vol. 17, No. 1, 2007, pp. 345-352.
doi:10.1016/j.dsp.2006.01.003

[12]
H. Kar, “Comments on ‘New LMI Condition for the Nonexistence of Overflow Oscillations in 2-D State-Space Digital Filters Using Saturation Arithmetic’,” Digital Signal Process, Vol. 18, No. 2, 2008, pp. 148-150.
doi:10.1016/j.dsp.2007.02.001

[13]
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

[14]
R. Yang, L. Xie and C. Zhang, “*H*_{2} 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

[15]
A. Dhawan and H. Kar, “An LMI Approach to Robust Optimal Guaranteed Cost Control of 2-D Discrete Systems described by the Roesser Model,” Signal Process, Vol. 90, No. 9, 2010, pp. 2648-2654.
doi:10.1016/j.sigpro.2010.03.008

[16]
D. Yue and J. Lam, “Non-Fragile Guaranteed Cost Control for Uncertain Descriptor Systems with Time-Varying State and Input Delays,” Optimal Control Applications & Methods, Vol. 26, 2005, pp. 85-105. doi:10.1002/oca.753

[17]
L. H. Keel and S. P. Bhattacharya, “Robust, Fragile or Optimal,” IEEE Transactions on Automatic Control, Vol. 42, No. 8, 1997, pp. 1098-1105. doi:10.1109/9.618239

[18]
W. M. Haddad and J. R. Corrado, “Robust Resilient Dynamic Controllers for Systems with Parameter Uncertainty and Controller Gain Variations,” International Journal of Control, Vol. 73, No. 15, 2000, pp. 1405-1423.
doi:10.1080/002071700445424

[19]
C. Lien, W. Cheng, C. Tsai and K. Yu., “Non-Fragile Observer-Based Controls of Linear System via LMI Approach,” Chaos, Solitons and Fractals, Vol. 32, No. 4, 2007, pp. 1530-1537. doi:10.1016/j.chaos.2005.11.092

[20]
S. Xu, J. Lam, G. Yang and J. Wang, “Stabilization and *H*_{oo} Control for Uncertain Stochastic Time-Delay Systems via Non-Fragile Control,” Asian Journal of Control, Vol. 8, No. 2, 2006, pp. 197-200.
doi:10.1111/j.1934-6093.2006.tb00270.x

[21]
J. H. Park, “Robust Non-Fragile Control for Uncertain Discrete-Delay Large-Scale Systems with a Class of Controller Gain Variations,” Applied Mathematics and Computation, Vol. 149, No.1, 2004, pp. 147-164.
doi:10.1016/S0096-3003(02)00962-1

[22]
C. Lien, “*H*_{oo} Non-Fragile Observer-Based Controls of Dynamical Systems via LMI Optimization Approach,” Chaos, Solitons and Fractals, Vol. 34, No. 2, 2007, pp. 428-436. doi:10.1016/j.chaos.2006.03.050

[23]
C. Lien, “Non-Fragile Guaranteed Cost Control for Uncertain Neutral Dynamic Systems with Time-Varying Delays in State and Control Input,” Chaos, Solitons and Fractals, Vol. 31, No. 4, 2007, pp. 889-899.
doi:10.1016/j.chaos.2005.10.080

[24]
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

[25]
P. Gahinet, A. Nemirovski, A. J. Laub and M. Chilali, “LMI Control Toolbox—For Use with Matlab,” The MATH Works Inc., Natick, MA, 1995.