Behavioral Systems Theory: A Survey

Aleixo J. C., Polderman J. W. and Rocha P. (2007). Representations and structural properties of periodic systems, Automatica43(11): 1921-1931.10.1016/j.automatica.2007.03.013Search in Google Scholar

Bourlès H. (2005). Structural properties of discrete and continuous linear time-varying systems, in F. Lamnabhi-Lagarrigue A. Loria E. Panteley (Eds.), Advanced Topics in Control Systems Theory, Springer, London.10.1007/11334774_6Search in Google Scholar

Chyzak F., Quadrat A. and Robertz D. (2005). Effective algorithms for parametrizing linear control systems over Ore algebras, Applicable Algebra in Engineering, Communication and Computing16(5): 319-376.10.1007/s00200-005-0188-6Search in Google Scholar

Fuhrmann P. A. (2002). A study of behaviors, Linear Algebra and its Applications351-352: 303-380.10.1016/S0024-3795(02)00282-3Search in Google Scholar

Fuhrmann P. A., Rapisarda P. and Yamamoto Y. (2007). On the state of behaviors, Linear Algebra and its Applications424(2-3): 570-614.10.1016/j.laa.2007.02.028Search in Google Scholar

Ilchmann A. and Mehrmann V. (2005). A behavioral approach to time-varying linear systems, SIAM Journal on Control and Optimization44(5): 1725-1747.10.1137/S0363012904442239Search in Google Scholar

Kuijper M. and Polderman J. W. (2004). Reed-Solomon list decoding from a system-theoretic perspective, IEEE Transactions on Information Theory50(2): 259-271.10.1109/TIT.2003.822593Search in Google Scholar

Kuijper M., Pinto R., Polderman J. W. and Rocha P. (2006). Autonomicity and the absence of free variables for behaviors over finite rings, Proceedings of the 7th Portuguese Conference on Automatic Control (Controlo 2006), Lisbon, Portugal.Search in Google Scholar

Lomadze V. (2007). When are linear differentiation-invariant spaces differential? Linear Algebra and its Applications424(2-3): 540-554.10.1016/j.laa.2006.06.031Search in Google Scholar

Lu P., Liu M. and Oberst U. (2004). Linear recurring arrays, linear systems and multidimensional cyclic codes over quasi-Frobenius rings, Acta Applicandae Mathematicae80(2): 175-198.10.1023/B:ACAP.0000013854.77539.53Search in Google Scholar

Oberst U. (1990). Multidimensional constant linear systems, Acta Applicandae Mathematicae20(1-2): 1-175.10.1007/BF00046908Search in Google Scholar

Oberst U. (2006). Stability and stabilization of multidimensional input/output systems, SIAM Journal on Control and Optimization45(4): 1467-1507.10.1137/050639004Search in Google Scholar

Pillai H. K. and Shankar S. (1999). A behavioral approach to control of distributed systems, SIAM Journal on Control and Optimization37(2): 388-408.10.1137/S0363012997321784Search in Google Scholar

Polderman J. W. and Willems J. C. (1998): Introduction to Mathematical Systems Theory, Springer, New York, NY.10.1007/978-1-4757-2953-5Search in Google Scholar

Pommaret J. F. and Quadrat A. (1998). Generalized Bézout identity, Applicable Algebra in Engineering, Communication and Computing9(2): 91-116.10.1007/s002000050096Search in Google Scholar

Pommaret J. F. and Quadrat A. (1999). Algebraic analysis of linear multidimensional control systems, IMA Journal of Mathematical Control and Information16(3): 275-297.10.1093/imamci/16.3.275Search in Google Scholar

Praagman C., Trentelman H. L. and Zavala Yoe R. (2007). On the parametrization of all regularly implementing and stabilizing controllers, SIAM Journal on Control and Optimization45(6): 2035-2053.10.1137/050628696Search in Google Scholar

Rapisarda P. and Willems J. C. (1997). State maps for linear systems, SIAM Journal on Control and Optimization35(3):1053-1091.10.1137/S0363012994268412Search in Google Scholar

Rocha P. (1990). Structure and representation of 2-D systems, Ph. D. thesis, University of Groningen.Search in Google Scholar

Rocha P. and Wood J. (1997). A new perspective on controllability properties for dynamical systems, International Journal of Applied Mathematics and Computer Science7(4): 869-879.Search in Google Scholar

Shankar S. (2002). The evolution of the concept of controllability, Mathematical and Computer Modelling of Dynamical Systems8(4): 397-406.10.1076/mcmd.8.4.397.15845Search in Google Scholar

Valcher M. E. and Willems J. C. (1999). Observer synthesis in the behavioral approach, IEEE Transactions on Automatic Control44(12): 2297-2307.10.1109/9.811213Search in Google Scholar

Willems J. C. (1986/87). From time series to linear system. Part I: Automatica22: 561-580, Part II: Automatica22: 675-694, Part III: Automatica23: 87-115.10.1016/0005-1098(86)90005-1Search in Google Scholar

Willems J. C. (1991). Paradigms and puzzles in the theory of dynamical systems, IEEE Transactions of Automatic Control36(3): 259-294.10.1109/9.73561Search in Google Scholar

Willems J. C. and Yamamoto Y. (2007). Representations of linear time-invariant behaviors by rational functions, Linear Algebra and its Applications425(2-3): 226-241.10.1016/j.laa.2006.12.020Search in Google Scholar

Wood J., Rogers E. and Owens D. H. (1999). Controllable and autonomous nD linear systems, Multidimensional Systems and Signal Processing10(1): 33-69.10.1023/A:1008409002248Search in Google Scholar

Wood J. (2000). Modules and behaviours in nD systems theory, Multidimensional Systems and Signal Processing11(1-2): 11-48.10.1023/A:1008430528456Search in Google Scholar

Zerz E. (2000). Topics in Multidimensional Linear Systems Theory, Springer, London.Search in Google Scholar

Zerz E. (2006). An algebraic analysis approach to linear timevarying systems, IMA Journal of Mathematical Control and Information23(1): 113-126.10.1093/imamci/dni047Search in Google Scholar

Zerz E. (2007). Autonomy properties of multidimensional linear systems over rings, Proceedings of the 5th International Workshop on Multidimensional Systems (NDS 2007), Aveiro, Portugal.10.1109/NDS.2007.4509547Search in Google Scholar