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Original Articles

Subspace algorithms for identifying separable-in-denominator 2D systems with deterministic–stochastic inputs

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Pages 2584-2610 | Received 22 Sep 2015, Accepted 26 Mar 2016, Published online: 28 Jul 2016

References

  • Aboutalib, A.O., & Silverman, L.M. (1975). Restoration of motion degraded images. IEEE Transactions on Circuits and Systems, 22, 278–286.
  • Abramatic, J., Attasi, S., Chieze, J., & Curien, N. (1975). Modèles statistiques bidimensionnels et application au traitement numérique des images. In Colloque national sur le traitement du signal et ses applications (pp. 117–124). Nice.
  • Ali, M., Chughtai, S.S., & Werner, H. (2009, December). Identification of spatially interconnected systems. In Proceedings of the 48th IEEE Conference on Decision and Control, held jointly with the 2009 28th Chinese Control Conference (pp. 7163–7168). Shanghai, China.
  • Anderson, B.D.O., Agathoklis, P., Jury, E.I., & Mansour, M. (1986). Stability and the matrix Lyapunov equation for discrete 2-dimensional systems. IEEE Transactions on Circuits and Systems, 33, 261–267.
  • Antoniou, G.E., Paraskevopoulos, P.N., & Varoufakis, S.J. (1988). Minimal state-space realization of factorable 2-D transfer functions. IEEE Transactions on Circuits and Systems, 35, 1055–1058.
  • Attasi, S. (1976). Modelling and recursive estimation for double indexed sequences. In R. Mehra & D. Lainiotis (Eds.), System identification: Advances and case studies (pp. 289–348). New York, NY: Academic Press.
  • Azimi-Sadjadi, M., & Wong, P. (1987). Two-dimensional block Kalman filtering for image restoration. IEEE Transactions on Acoustics, Speech, and Signal Processing, 35, 1736–1749.
  • Barry, P., Gran, R., & Waters, C. (1976, December). Two-dimensional filtering: A state space approach. In Proceedings of the IEEE Conference on Decision and Control (pp. 613–618). Clearwater, FL.
  • Chen, C., Tsai, J., & Shieh, L. (2003). Modeling of variable coefficient Roesser's model for systems described by second order partial differential equation. Circuits, Systems, and Signal Processing, 22, 423–463.
  • Cichy, B., Galkowski, K., Rogers, E., & Kummert, A. (2013). Control law design for discrete linear repetitive processes with non-local updating structures. Multidimensional Systems and Signal Processing, 24, 707–726.
  • Clara, F., Silverman, L.M., & Abramatic, J.F. (1982). Nonlinear image restoration: A visual quality constrained approach. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 1982), 7, 2098–2101.
  • Cunha, D.P. (2013). Reduced order state-space models for 2-D systems (Master's thesis). University of Porto.
  • D’Andrea, R., & Dullerud, G.E. (2003). Distributed control design for spatially interconnected systems. IEEE Transactions on Automatic Control, 48, 1478–1495.
  • Dillabough, M. (2007). Discrete state-space models for distributed parameter systems (Master's thesis). School of Graduate Studies Laurentian University, Sudbury.
  • Dillabough, M., Shang, H., & McLellan, P.J. (2006, April). A state space approach for boundary control of distributed parameter systems. In International Symposium on Advanced Control of Chemical Processes (ADCHEM 2006) (pp. 341–346). Gramado, Brazil.
  • Ding, T., Sznaier, M., & Camps, O. (2006, December). Robust identification of 2-D periodic systems with applications to texture synthesis and classification. In Proceedings of the IEEE Conference on Decision and Control (pp. 3678–3683). San Diego, CA.
  • Farah, M., Mercère, G., Ouvrard, R., Poinot, T., & Ramos, J. (2014, June). Identification of 2-D Roesser models by using linear fractional representations. In Proceedings of the European Control Conference (pp. 382–387). Strasbourg.
  • Fornasini, E., & Marchesini, G. (1978). Doubly-indexed dynamical systems: state-space models and structural properties. Mathematical Systems Theory, 12, 59–72.
  • Fraanje, R., & Verhaegen, M. (2005, July). A spatial canonical approach to multidimensional state-space identification for distributed parameter systems. In Proceedings of the International Workshop on Multidimensional Systems (pp. 217–222). Wuppertal.
  • Galkowski, K. (2000). Higher order discretization of 2-D systems. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 47, 713–722.
  • Givone, D., & Roesser, R. (1972). Multidimensional linear iterative circuits – general properties. IEEE Transactions on Computers, 21, 1067–1073.
  • Habibi, A. (1972). Two-dimensional Bayesian estimate of images. Proceedings of the IEEE, 60, 878–883.
  • Hidayat, Z., Nunez, A., Babuska, R., & Schutter, B.D. (2012, October). Identification of distributed-parameter systems with missing data. In Proceedings of the IEEE International Conference on Control Applications (pp. 1014–1019). Dubrovnik, Croatia.
  • Hinamoto, T. (1980). Realizations of a state-space model from two-dimensional input–output map. IEEE Transactions on Circuits and Systems, 27, 36–44.
  • Hinamoto, T. (1981). On the partial realization from two-dimensional input–output map. IEEE Transactions on Circuits and Systems, 28, 345–347.
  • Janczak, A., Rogers, E., & Cai, Z. (2013, September). Subspace identification of process dynamics for iterative learning control. In Proceedings of the 8th International Workshop on Multidimensional Systems (nDS) (pp. 1–6). Erlangen, Germany.
  • Kaczorek, T. (1985). Two dimensional linear systems. Berlin: Springer Verlag.
  • Kailath, T. (1980). Linear systems. Englewood Cliffs, NJ: Prentice-Hall.
  • Katayama, T. (2005). Subspace methods for system identification. London: Springer Verlag.
  • Katayama, T. (2010, June). Subspace identification of combined deterministic-stochastic systems by LQ decomposition. In Proceedings of the American Control Conference (pp. 2941–2946). Baltimore, MD.
  • Katayama, T., & Kosaka, M. (1979). Recursive filtering algorithm for a two-dimensional system. IEEE Transactions of Automatic Control, 24, 130–132.
  • Katayama, T., & Picci, G. (1999). Realization of stochastic systems with exogenous inputs and subspace identification methods. Automatica, 35, 1635–1652.
  • Kung, S.Y., Levy, B.C., Morf, M., & Kailath, T. (1977). New results in 2-D system theory. Part II: 2-D state-space models-realization and the notions of controllability, observability, and minimality. Proceedings of the IEEE, 65, 945–961.
  • Kurek (1985). The general state-space model for a two-dimensional linear digital system. IEEE Transactions on Automatic Control, 30, 600–602.
  • Kurek, J.E.& Zaremba, M. (1993). Iterative learning control synthesis based on 2-D system theory. IEEE Transactions on Automatic Control, 38, 121–125.
  • Larimore, W.E. (1983, June). System identification, reduced-order filtering and modeling via canonical variate analysis. In Proceedings of the American Control Conference (pp. 445–451). San Francisco, CA.
  • Lashgari, B. (1981). Two-dimensional approximation, model reduction and minimum variance error estimation. Los Angeles: University of Southern California.
  • Lashgari, B., & Silverman, L. (1986). Recursive estimation of two-dimensional processes with application to image processing. Circuits Systems and Signal Processing, 5, 212–226.
  • Lashgari, B., Silverman, L., & Abramatic, J. (1983). Approximation of 2-D separable in denominator filters. IEEE Transactions on Circuits and Systems, 30, 107–121.
  • Lele, S., & Mendel, J. (1987). Modeling and recursive state estimation for two-dimensional noncausal filters with applications in image restoration. IEEE Transactions on Circuits and Systems, 34, 1507–1517.
  • Lin, T., & Kawamata, M. (1985). A counterexample to 2-D Lyapunov equations by Mertzios. IEEE Transactions on Circuits and Systems, 32, 1310–1311.
  • Lin, T., Kawamata, M., & Higuchi, T. (1987). Decomposition of 2-D separable-denominator systems: existence, uniqueness, and applications. IEEE Transactions on Circuits and Systems, 34, 292–296.
  • Lu, W.S., & Antoniou, A. (1986). Synthesis of 2-D state-space fixed-point digital-filter structures with minimum roundoff noise. IEEE Transactions on Circuits and Systems, 33, 965–973.
  • Magnus, J., & Neudecker, H. (2001). Matrix differential calculus with applications in statistics and econometrics. Chichester: John Wiley & Sons.
  • Marszalek, W. (1984). Two-dimensional state-space discrete models for hyperbolic partial differential equations. Applied Mathematical Modelling, 8, 11–14.
  • Martin, C. (2005). Higher-order Kronecker products and tensor decompositions. Ithaca, NY: Cornell University.
  • Morf, M., Levy, B.C., & Kung, S.Y. (1977). New results in 2-D systems theory. Part I: 2-D polynomial matrices, factorization, and coprimeness. Proceedings of the IEEE, 65, 861–872.
  • Ng, M., & Plemmons, R. (2007). Blind deconvolution and structured matrix computations with applications to array imaging. In P. Campisi & K. Egiazarian, (Eds.), Blind image deconvolution: Theory and applications (pp. 377–418). CRC Press.
  • Owens, D., Amann, N., Rogers, E., & French, M. (2000). Analysis of linear iterative learning control schemes - A 2-D systems/repetitive processes approach. Multidimensional Systems and Signal Processing, 11, 125–177.
  • Qin, S.J., Lin, W., & Ljung, L. (2005). A novel subspace identification approach with enforced causal models. Automatica, 41, 2043–2053.
  • Ramos, J. (1994). A subspace algorithm for identifying 2-D separable-in-denominator filters. IEEE Transactions on Circuits and Systems, 41, 63–67.
  • Ramos, J., Alenany, A., Shang, H., & Lopes dos Santos, P. (2011). Subspace algorithms for identifying separable in denominator 2-D systems with deterministic inputs. IET Control Theory and Applications, 5, 1748–1768.
  • Rice, J.K., & Verhaegen, M. (2011). Efficient system identification of heterogeneous distributed systems via a structure exploiting extended Kalman filter. IEEE Transactions on Automatic Control, 56, 1713–1718.
  • Roesser, R. (1975). A discrete-state-space model for linear image processing. IEEE Transactions on Automatic Control, 20, 1–10.
  • Schorsch, J., Garnier, H., Gilson, M., & Young, P.C. (2013). Instrumental variable methods for identifying partial differential equation models. International Journal of Control, 86, 2325–2335.
  • Treasure, R., Sreeram, V., & Ngan, K.N. (2004). Balanced identification and model reduction of a separable denominator 2-D system. 5th Asian Control Conference, 3, 2048–2052.
  • Turkington, D.A. (2000). Generalised vec operators and the seemingly unrelated regression equations model with vector correlated disturbances. Journal of Econometrics, 99, 225–253.
  • van Overschee, P., & de Moor, B. (1996). Subspace identification for linear systems. Theory, implementation, and applications. Dordrecht: Kluwer Academic.
  • Verhaegen, M. (1994). Identification of the deterministic part of MIMO state space model given in innovations form from input-output data. Automatica, 30, 61–74.
  • Verhaegen, M., & Verdult, V. (2007). Filtering and system identification: A least squares approach. New York, NY: Cambridge University Press.
  • Wang, D., & Zilouchian, A. (1999). Identification of two-dimensional state space discrete systems using neural networks. In S.G. Zsafestas (Ed.), Soft Computing in Systems and Control Technology (Vol. 18, pp. 31–51). World Scientific.
  • Wang, D., Zilouchian, A., Zhao, J., & Huang, Z. (2007). Modular structure realizations of 2-D separable-in-denominator recursive digital filters. Signal Processing, 87, 2686–2694.
  • Wirski, R.T. (2008). On the realization of 2-D orthogonal state-space systems. Signal Processing, 88, 2747–2753.
  • Xiao, C., Sreeram, V., Liu, W., & Venetsanopolos, A. (1998). Identification and model reduction of 2-D systems via the extended impulse response gramians. Automatica, 34, 93–101.
  • Xu, S., Lam, J., L., Z., Galkowski, K., Paszke, W., Sulikowski, B., ... Owens, D.H. (2003). Positive real control of two-dimensional systems: Roesser models and linear repetitive processes. International Journal of Control, 76, 1047–1058.
  • Yang, R., Xie, L., & Zhang, C. (2006). H2 and mixed H2/H∞ control of two-dimensional systems in Roesser Model. Automatica, 42, 1507–1514.

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