Triangular representation of Fornasini–Marchesini systems

Alpay D., Dubi C. (2003) A realization theorem for functions of several complex variables. System and Control Letters 49: 225–229 Alpay D., Dubi C. (2003) Backward shift operators and finite dimensional de Branges Rovnyak spaces in the ball. Linear Algebra and its Applications 371: 277–285 Alpay D., Dubi C. (2005) On commuting operators solving Gleason’s problem. Proceedings of AMS 133(11): 3285–3293 Ball J.A., Groenewald G., Malakorn T. (2005) Structured noncommutative multidimensional linear systems. SIAM Journal of Control Optimimization 44(4): 1474–1528 Ball J.A., Sadosky C., Vinnikov V. (2005) Conservative input-state-output systems with evolution on a multidimensional integer lattice. Multidimensional Systems and Signal Processing 16: 133–198 Bisiacco M., Valcher E.M. (2006) Observer-based fault detection and isolation for 2D state-space models. Multidimensional Systems and Signal Processing 17: 219–242 Dubi C. (2007) Weak simultaneous triangularization – a determinant condition. Operators and Matrices 1(1): 527–534 Dubi C. (2008) Triangular realization of rational functions of N complex variables. Multidimensional Systems and Signal Processing 19(1): 123–129 Dymkov M., Gaishun I., Rogers E., Galkowski K., Owens D.H. (2003) Z-transform and volterra-operator based approaches to controllability and observability analysis for discrete linear repetitive processes. Multidimensional Systems and Signal Processing 14: 365–395 Fornasini E., Marchesini G. (1976) State-space realization theory of two-dimensional filters. IEEE Transactions on Automatic Control 21: 484–492 Fornasini E., Marchesini G. (1978) Doubly-indexed dynamical systems: State-space models and structural properties. Mathamatical Systems Theory 12: 59–72 Galkowski K., Rogers E., Owens D.H. (1999) New 2D models and a transition matrix for discrete linear repetitive processes. International Journal of Control 72(15): 1365–1380 Galkowski K., Lam J., Xu S., Lin Z. (2001) LMI approach to state–feedback stabilization of multidimensional systems. International Journal of Control 76(14): 1428–1436 Galkowski K, Rogers E, Paszke W, Owens D.H. (2003). Linear repetitive process control theory applied to a physicalexample. International Journal of Applied Mathematics andComputer Science 13(1): 87–99 Gohberg, I., Lancaster, P., & Rodman, L. (1986). Invariant subspaces of matrices with applications. Canadian Mathematical Society Series of Monographs and Advanced Texts. Gorbatsevich V.V., Onishichik A.L., Vinberg E.B. (1994) Structure of lie groups and lie algebras. Springer-Verlag, Berlin, Germany Jury, E. L. (1978). Stability of multidimensional scalar and matrix polynomials. Proceedings of the IEEE, 66(9). Miri S.A., Aplevich J.D. (1998) Equivalence of n-dimensional Rosser and Fornasini–Marchesini models. IEEE Transactions on Automatic Control 43(3): 401–405 Ooba T. (2001) Stabilization of multidimensional systems using local state estimator. Multidimensional Systems and Signal Processing 12: 49–61 Ooba T. (2001) On stability robustness of 2D systems described by the Fornasini-Marchesini model. Multidimensional Systems and Signal Processing 12: 49–61 Radjavi H. (1986) A Trace condition equivalent to simultaneous triangularizability. Canadian Journal of Mathamatics 38(2): 376–386 Radjavi H., Rosenthal P. (2000) Simultaneous triangularization. Springer-Verlag, New-York Rogers E., Galkowski K., Owens D.H. (1992) Stability analysis for linear repetitive processes: lecture notes in control and information sciences (Vol. 175). Springer, Berlin/Heidelberg Rogers, E., Galkowski, K., Owens, D.H. (2007). Control systems theory and applications for linear repetitive processes series. Lecture Notes in Control and Information Sciences (Vol. 349). Springer. Rudin, W. (1980). Function theory in the unit ball of \({{\mathbb{C}}^n}\). Springer-Verlag. Samelson H. (1969) Notes on lie algebra. Van Nostrand Reinhold, New-York