Robust state feedback $$H_\infty $$ H ∞ control for uncertain 2-D continuous state delayed systems in the Roesser model

Benhayoun, M., Benzaouia, A., Mesquine, F., & Tadeo, F. (2010). Stabilization of 2D continuous systems with multi-delays and saturated control. In Proceedings of the 18th mediterranean conference on control and automation (pp. 993–999). Morocco: Marrakech, 23–25 June.

Benhayoun, M., Mesquine, F., & Benzaouia, A. (2013). Delay-dependent stabilizability of 2D delayed continuous systems with saturating control. Circuits, Systems, and Signal Processing, 32(6), 2723–2743.

Benzaouia, A., Benhayoun, M., & Tadeo, F. (2011). State feedback stabilization of 2-D continuous systems with delays. International Journal of Innovative Computing, Information and Control, 7(2), 977–988.

Boukili, B., Hmamed, A., Benzaouia, A., & El Hajjaji, A. (2014). $$H_\infty $$ H ∞ filtering of two-dimensional TS fuzzy systems. Circuits, Systems, and Signal Processing, 33(6), 1737–1761.

Boyd, S. P., El Ghaoui, L., Feron, E., & Balakrishnan, V. (1994). Linear matrix inequalities in system and control theory. Philadelphia: Society for Industrial & Applied.

Chen, S. F. (2010). Delay-dependent stability for 2D systems with time-varying delay subject to state saturation in the Roesser model. Applied Mathematics and Computation, 216(9), 2613–2622.

Dymkou, S., Rogers, E., Dymkov, M., & Galkowski, K. (2008). Constrained optimal control theory for differential linear repetitive processes. SIAM Journal of Control and Optimization, 47(1), 396–420.

Du, C., & Xie, L. (1999). Stability analysis and stabilization of uncertain two-dimensional discrete systems: An LMI approach. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 46(11), 1371–1374.

Du, C., & Xie, L. (2002). $$H_\infty $$ H ∞ control and filtering of two-dimensional systems. Berlin: Springer.

Duan, Z., Xiang, Z., & Karimi, H. R. (2013). Delay-dependent $$H_\infty $$ H ∞ control for 2-D switched delay systems in the second FM model. Journal of the Franklin Institute, 350(7), 1697–1718.

El-Kasri, C., & Hmamed, A. (2013). Robust reduced-order $$H_\infty $$ H ∞ filter design for uncertain 2-D continuous systems with time-varying delays. In Proceedings of 3rd IEEE international conference on systems and control (ICSC) (pp. 545–550). Algiers, 29–31 October.

El-Kasri, C., Hmamed, A., Tissir, E. H., & Tadeo, F. (2013). Robust $$H_\infty $$ H ∞ filtering for uncertain two-dimensional continuous systems with time-varying delays. Multidimensional Systems and Signal Processing, 24(4), 685–706.

El-Kasri, C., Hmamed, A., Tissir, H., & Tadeo, F. (2012). Uncertain 2-D continuous systems with state delay: Filter design using $$H_\infty $$ H ∞ polynomial approach. International Journal of Computer Applications, 44(18), 0975–8887.

Emelianova, J., Pakshin, P., Gałkowski, K., & Rogers, E. (2014). Stability of nonlinear 2-D systems described by the continuous-time Roesser model. Automation and Remote Control, 75(5), 845–858.

Fan, H., & Wen, C. (2002). A sufficient condition on the exponential stability of two-dimensional (2-D) shift-variant systems. IEEE Transactions on Automatic Control, 47(4), 647–655.

Feng, Z.-Y., Wu, Q., & Xu, L. (2012). $$H_\infty $$ H ∞ control of linear multidimensional discrete systems. Multidimensional Systems and Signal Processing, 23(3), 381–411.

Galkowski, K., Paszke, W., Sulikowski, B., Rogers, E., & Owens, D. (2002). LMI based stability analysis and controller design for a class of 2-D continuous-discrete linear systems. In Proceedings of IEEE American control conference (pp. 29–34). Anchorage, AK, 8–10 May.

Ghamgui, M., Yeganefar, N., Bachelier, O., & Mehdi, D. (2011a). Exponential stability conditions for 2-D continuous state-delayed systems. In 7th IEEE International workshop on multidimensional (nD) systems (nDs) (pp. 1–5). Poitiers, 5–7 September.

Ghamgui, M., Yeganefar, N., Bachelier, O., & Mehdi, D. (2011b). Stability and stabilization of 2-D continuous state-delayed systems. In 50th IEEE conference on decision and control and European control conference (CDC-ECC) (pp. 1878–1883). Orlando, FL, 12–15 December.

He, Y., Wu, M., Liu, G.-P., & She, J.-H. (2008). Output feedback stabilization for a discrete-time system with a time-varying delay. IEEE Transactions on Automatic Control, 53(10), 2372–2377.

Hinamoto, T. (1997). Stability of 2-D discrete systems described by the Fornasini-Marchesini second model. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 44(3), 254–257.

Hmamed, A., El-Kasri, C., Tissir, E. H., Alvarez, T., & Tadeo, F. (2013). Robust $$H_\infty $$ H ∞ filtering for uncertin 2-D continuous systems with delays. International Journal of Innovative Computing, Information and Control, 9(5), 2167–2183.

Hmamed, A., Mesquine, F., Tadeo, F., Benhayoun, M., & Benzaouia, A. (2010). Stabilization of 2-D saturated systems by state feedback control. Multidimensional Systems and Signal Processing, 21(3), 277–292.

Huang, S., & Xiang, Z. (2013). Delay-dependent stability for discrete 2-D switched systems with state delays in the Roesser model. Circuits, Systems, and Signal Processing, 32(6), 2821–2837.

Kaczorek, T. (1985). Two-dimensional linear systems. Berlin: Springer.

Lam, J., Xu, S., Zou, Y., Lin, Z., & Galkowski, K. (2004). Robust output feedback stabilization for two-dimensional continuous systems in Roesser form. Applied Mathematics Letters, 17(12), 1331–1341.

Li, X., & Gao, H. (2011). A new model transformation of discrete-time systems with time-varying delay and its application to stability analysis. IEEE Transactions on Automatic Control, 56(9), 2172–2178.

Li, X., & Gao, H. (2012). Robust finite frequency $$H_\infty $$ H ∞ filtering for uncertain 2-D Roesser systems. Automatica, 48(6), 1163–1170.

Li, X., Gao, H., & Wang, C. (2012). Generalized Kalman–Yakubovich–Popov lemma for 2-D FM LSS model. IEEE Transactions on Automatic Control, 57(12), 3090–3103.

Lin, Z., Lam, J., Galkowski, K., & Xu, S. (2001). A constructive approach to stabilizability and stabilization of a class of nD systems. Multidimensional Systems and Signal Processing, 12(3–4), 329–343.

Lu, W.-S. (1992). Two-dimensional digital filters. Boca Raton: CRC Press.

Paszke, W., Lam, J., Gałkowski, K., Xu, S., & Lin, Z. (2004). Robust stability and stabilisation of 2D discrete state-delayed systems. Systems & Control Letters, 51(3), 277–291.

Paszke, W., Lam, J., Galkowski, K., Xu, S., Rogers, E., & Kummert, A. (2006). Delay-dependent stability of 2D state-delayed linear systems. In Proceedings of IEEE international symposium on circuits and systems (pp. 2813–1816). Island of Kos, 21–24 May.

Roesser, R. P. (1975). A discrete state-space model for linear image processing. IEEE Transactions on Automatic Control, 20(1), 1–10.

Shaker, H. R., & Shaker, F. (2014). Lyapunov stability for continuous-time multidimensional nonlinear systems. Nonlinear Dynamics, 75(4), 717–724.

Xie, L. (1996). Output feedback $$H_\infty $$ H ∞ control of systems with parameter uncertainty. International Journal of Control, 63(4), 741–750.

Xu, H., Lin, Z., & Makur, A. (2012). The existence and design of functional observers for two-dimensional systems. Systems & Control Letters, 61(2), 362–368.

Xu, L., Lin, Z., Ying, J. Q., Saito, O., & Anazawa, Y. (2004). Open problems in control of linear discrete multidimensional systems. In B. Vincent & M. Alexander (Eds.), Unsolved problems in mathematical systems and control theory Part 6 (pp. 212–220). Princeton: Princeton University Press.

Xu, H., Zou, Y., Lu, J., & Xu, S. (2005a). Robust $$H_\infty $$ H ∞ control for a class of uncertain nonlinear two-dimensional systems with state delays. Journal of the Franklin Institute, 342(7), 877–891.

Xu, H., Zou, Y., & Xu, S. (2005b). Robust $$H_\infty $$ H ∞ control for a class of uncertain nonlinear two-dimensional systems. International Journal of Innovative Computing, Information and Control, 1(2), 181–191.

Xu, H., Zou, Y., Xu, S., & Guo, L. (2008). Robust $$H_\infty $$ H ∞ control for uncertain two-dimensional discrete systems described by the general model via output feedback controllers. International Journal of Control, Automation, and Systems, 6(5), 785–791.

Xu, J., Nan, Y., Zhang, G., Ou, L., & Ni, H. (2013). Delay-dependent $$H_\infty $$ H ∞ control for uncertain 2-D discrete systems with state delay in the Roesser model. Circuits, Systems, and Signal Processing, 32(3), 1097–1112.

Xu, S., Lam, J., Zou, Y., Lin, Z., & Paszke, W. (2005). Robust $$H_\infty $$ H ∞ filtering for uncertain 2-D continuous systems. IEEE Transactions on Signal Processing, 53(5), 1731–1738.

Yan, H., Zhang, H., & Meng, M. Q.-H. (2010). Delay-range-dependent robust $$H_\infty $$ H ∞ control for uncertain systems with interval time-varying delays. Neurocomputing, 73(7), 1235–1243.

Yang, R., Xie, L., & Zhang, C. (2008). Generalized two-dimensional Kalman–Yakubovich–Popov lemma for discrete Roesser model. IEEE Transactions on Circuits and Systems I: Regular Papers, 55(10), 3223–3233.

Ye, S., Li, J., & Yao, J. (2014). Robust $$H_\infty $$ H ∞ control for a class of 2-D discrete delayed systems. ISA Transactions. doi: 10.1016/j.isatra.2013.12.017 .

Zames, G. (1981). Feedback and optimal sensitivity: Model reference transformations, multiplicative seminorms, and approximate inverses. IEEE Transactions on Automatic Control, 26(2), 301–320.