Dissipative stability analysis and control of two-dimensional Fornasini–Marchesini local state-space model

References

• Ahn, C.K., Shi, P., & Basin, M.V. (2015). Two-dimensional dissipative control and filtering for Roesser model. IEEE Transactions on Automatic Control, 60(7), 1745–1759.
   Web of Science ®Google Scholar
• de Souza, C.E., Xie, L., & Coutinho, D.F. (2010). Robust filtering for 2-D discrete-time linear systems with convex-bounded parameter uncertainty. Automatica, 46(4), 673–681.
   Web of Science ®Google Scholar
• Ding, D., Du, X., & Li, X. (2015). Finite-frequency model reduction of two-dimensional digital filters. IEEE Transactions on Automatic Control, 60(6), 1624–1629.
   Web of Science ®Google Scholar
• Du, C., & Xie, L. (1999). LMI approach to output feedback stabilization of 2-D discrete systems. International Journal of Control, 72(2), 97–106.
   Web of Science ®Google Scholar
• Du, C., & Xie, L. (2002). H_∞ control and filtering of two-dimensional systems. New York: Springer.
   Google Scholar
• Du, C., Xie, L., & Soh, Y.C. (2000). H∞ filtering of 2-D discrete systems. IEEE Transactions on Signal Processing, 48(6), 1760–1768.
   Web of Science ®Google Scholar
• Ebihara, Y., Ito, Y., & Hagiwara, T. (2006). Exact stability analysis of 2-D systems using LMIs. IEEE Transactions on Automatic Control, 51(9), 1509–1513.
   Web of Science ®Google Scholar
• Feng, Z., & Lam, J. (2011). Stability and dissipativity analysis of distributed delay cellular neural networks. IEEE Transactions on Neural Networks, 22(6), 976–981.
   PubMed Web of Science ®Google Scholar
• Feng, Z., Lam, J., & Gao, H. (2011). α-Dissipativity analysis of singular time-delay systems. Automatica, 47(11), 2548–2552.
   Web of Science ®Google Scholar
• Fornasini, E., & Marchesini, G. (1978). Doubly indexed dynamical systems: State-space models and structural properties. Mathematical Systems Theory, 12(1), 59–72.
   Google Scholar
• Fu, P., Chen, J., & Niculescu, S.I. (2006). Generalized eigenvalue-based stability tests for 2-D linear systems: Necessary and sufficient conditions. Automatica, 42(9), 1569–1576.
   Web of Science ®Google Scholar
• Gahinet, P., & Apkarian, P. (1994). A linear matrix inequality approach to H∞ control. International Journal of Robust Nonlinear Control, 4(4), 421–448.
   Web of Science ®Google Scholar
• Gao, H., Lam, J., Wang, C., & Xu, S. (2005). H∞ model reduction for uncertain two-dimensional discrete systems. Optimal Control Applications and Methods, 26(4), 199–227.
   Web of Science ®Google Scholar
• Hill, D.J., & Moylan, P.J. (1980). Dissipative dynamical systems: Basic input-output and state properties. Journal of the Franklin Institute, 309(5), 327–357.
   Web of Science ®Google Scholar
• 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.
   Google Scholar
• Iwasaki, T., & Hara, S. (2007). Feedback control synthesis of multiple frequency domain specifications via generalized KYP lemma. International Journal of Robust Nonlinear Control, 17(5–6), 415–434.
   Web of Science ®Google Scholar
• Kaczorek, T. (1985). Two-dimensional linear systems. Berlin: Springer.
   Google Scholar
• Li, X., & Gao, H. (2012). Robust finite frequency H∞ filtering for uncertain 2-D Roesser systems. Automatica, 48(6), 1163–1170.
   Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar
• Li, X., Lam, J., & Cheung, K.C. (2016). Generalized H∞ model reduction for stable two-dimensional discrete systems. Multidimensional Systems and Signal Processing, 27(2), 359–382.
   Web of Science ®Google Scholar
• Li, X., Lam, J., Gao, H., & Gu, Y. (2015). A frequency-partitioning approach to stability analysis of two-dimensional discrete systems. Multidimensional Systems and Signal Processing, 26(1), 67–93.
   Web of Science ®Google Scholar
• Li, Z., Wang, J., & Shao, H. (2002). Delay-dependent dissipative control for linear time-delay systems. Journal of the Franklin Institute, 339(6), 529–542.
   Web of Science ®Google Scholar
• Liang, J., Wang, Z., & Liu, X. (2015). H∞ control for 2-D time-delay systems with randomly occurring nonlinearities under sensor saturation and missing measurements. Journal of the Franklin Institute, 352(3), 1007–1030.
   Web of Science ®Google Scholar
• Lu, W.S., & Antoniou, A. (1992). Two-dimensional digital filters. New York: Marcel Dekker.
   Google Scholar
• Mahmoud, M.S., Nounou, H.N., & Xia, Y. (2010). Robust dissipative control for internet-based switching systems. Journal of the Franklin Institute, 347(1), 154–172.
   Web of Science ®Google Scholar
• Ntogramatzidis, L., & Cantoni, M. (2009). LQ optimal control for 2D Roesser models of finite extent. Systems and Control Letters, 58(7), 482–490.
   Web of Science ®Google Scholar
• Ooba, T. (2000). On stability of 2-D systems based on 2-D Lyapunov matrix inequalities. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 47(8), 1263–1265.
   Google Scholar
• Paszke, W., Lam, J., Galkowski, K., Xu, S., & Lin, Z. (2004). Robust stability and stabilisation of 2D discrete state-delayed systems. Systems and Control Letters, 51(3), 277–291.
   Web of Science ®Google Scholar
• Roesser, R.P. (1975). A discrete state-space model for linear image processing. IEEE Transactions on Automatic Control, 20(1), 1–10.
   Web of Science ®Google Scholar
• Rogers, E., & Owens, D.H. (1992). Stability analysis for linear repetitive processes. Berlin: Springer.
   Google Scholar
• Shen, H., Park, J.H., Zhang, L., & Wu, Z.G. (2014). Robust extended dissipative control for sampled-data Markov jump systems. International Journal of Control, 87(8), 1549–1564.
   Web of Science ®Google Scholar
• Su, X., Shi, P., Wu, L., & Basin, M. (2014). Reliable filtering with strict dissipativity for TS fuzzy time-delay systems. IEEE Transactions on Cybernetics, 44(12), 2470–2483.
   PubMed Web of Science ®Google Scholar
• Tan, Z., Soh, Y.C., & Xie, L. (1999). Dissipative control for linear discrete-time systems. Automatica, 35(9), 1557–1564.
   Web of Science ®Google Scholar
• Tuan, H.D., Apkarian, P., Nguyen, T.Q., & Narikiyo, T. (2002). Robust mixed H2/H∞ filtering of 2-D systems. IEEE Transactions on Signal Processing, 50(7), 1759–1771.
   Web of Science ®Google Scholar
• Wang, Q., Lam, J., Gao, H., & Wang, Q. (2006). Energy-to-peak model reduction for 2-d discrete systems in Fornasini–Marchesini form. European Journal of Control, 12(4), 420–430.
   Web of Science ®Google Scholar
• Willems, J. (1972). Dissipative dynamical systems part I: General theory. Archive for Rational Mechanics and Analysis, 45(5), 321–351.
   Web of Science ®Google Scholar
• Wu, L., Wang, Z., Gao, H., & Wang, C. (2007). Filtering for uncertain 2-D discrete systems with state delays. Signal Processing, 87(9), 2213–2230.
   Web of Science ®Google Scholar
• Wu, Z., Cui, M., Xie, X., & Shi, P. (2011). Theory of stochastic dissipative systems. IEEE Transactions on Automatic Control, 56(7), 1650–1655.
   Web of Science ®Google Scholar
• Xie, S., Xie, L., & Souza, C. (1998). Robust dissipative control for linear systems with dissipative uncertainty. International Journal of Control, 70(2), 169–191.
   Web of Science ®Google Scholar
• Xu, J., & Yu, L. (2009). Delay-dependent guaranteed cost control for uncertain 2-D discrete systems with state delay in the FM second model. Journal of the Franklin Institute, 346(2), 159–174.
   Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar