# Behavioral systems theory: A survey

International Journal of Applied Mathematics and Computer Science (2008)

- Volume: 18, Issue: 3, page 265-270
- ISSN: 1641-876X

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topEva Zerz. "Behavioral systems theory: A survey." International Journal of Applied Mathematics and Computer Science 18.3 (2008): 265-270. <http://eudml.org/doc/207883>.

@article{EvaZerz2008,

abstract = {We survey the so-called behavioral approach to systems and control theory, which was founded by J. C. Willems and his school. The central idea of behavioral systems theory is to put the focus on the set of trajectories of a dynamical system rather than on a specific set of equations modelling the underlying phenomenon. Moreover, all signal components are treated on an equal footing at first, and their partition into inputs and outputs is derived from the system law, in a way that admits several valid cause-effect interpretations, in general.},

author = {Eva Zerz},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {linear systems; behavioral approach},

language = {eng},

number = {3},

pages = {265-270},

title = {Behavioral systems theory: A survey},

url = {http://eudml.org/doc/207883},

volume = {18},

year = {2008},

}

TY - JOUR

AU - Eva Zerz

TI - Behavioral systems theory: A survey

JO - International Journal of Applied Mathematics and Computer Science

PY - 2008

VL - 18

IS - 3

SP - 265

EP - 270

AB - We survey the so-called behavioral approach to systems and control theory, which was founded by J. C. Willems and his school. The central idea of behavioral systems theory is to put the focus on the set of trajectories of a dynamical system rather than on a specific set of equations modelling the underlying phenomenon. Moreover, all signal components are treated on an equal footing at first, and their partition into inputs and outputs is derived from the system law, in a way that admits several valid cause-effect interpretations, in general.

LA - eng

KW - linear systems; behavioral approach

UR - http://eudml.org/doc/207883

ER -

## References

top- Aleixo J.C., Polderman J.W. and Rocha P. (2007). Representations and structural properties of periodic systems, Automatica 43(11): 1921-1931. Zbl1129.93031
- Bourlès H. (2005). Structural properties of discrete and continuous linear time-varying systems, in F. LamnabhiLagarrigue, A. Loria, E. Panteley (Eds.), Advanced Topics in Control Systems Theory, Springer, London. Zbl1167.93357
- Chyzak F., Quadrat A. and Robertz D. (2005). Effective algorithms for parametrizing linear control systems over Ore algebras, Applicable Algebra in Engineering, Communication and Computing 16(5): 319-376. Zbl1109.93018
- Fuhrmann P.A. (2002). A study of behaviors, Linear Algebra and its Applications 351-352: 303-380. Zbl1030.93010
- Fuhrmann P.A., Rapisarda P. and Yamamoto Y. (2007). On the state of behaviors, Linear Algebra and its Applications 424(2-3): 570-614. Zbl1114.93007
- Ilchmann A. and Mehrmann V. (2005). A behavioral approach to time-varying linear systems, SIAM Journal on Control and Optimization 44(5): 1725-1747. Zbl1139.93007
- Kuijper M. and Polderman J.W. (2004). Reed-Solomon list decoding from a system-theoretic perspective, IEEE Transactions on Information Theory 50(2): 259-271. Zbl1288.94113
- 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.
- Lomadze V. (2007). When are linear differentiation-invariant spaces differential? Linear Algebra and its Applications 424(2-3): 540-554. Zbl1136.93002
- Lu P., Liu M. and Oberst U. (2004). Linear recurring arrays, linear systems and multidimensional cyclic codes over quasiFrobenius rings, Acta Applicandae Mathematicae 80(2): 175-198. Zbl1082.94017
- Oberst U. (1990). Multidimensional constant linear systems, Acta Applicandae Mathematicae 20(1-2): 1-175. Zbl0715.93014
- Oberst U. (2006). Stability and stabilization of multidimensional input/output systems, SIAM Journal on Control and Optimization 45(4): 1467-1507. Zbl1123.93079
- Pillai H.K. and Shankar S. (1999). A behavioral approach to control of distributed systems, SIAM Journal on Control and Optimization 37(2): 388-408. Zbl0919.93020
- Polderman J.W. and Willems J.C. (1998): Introduction to Mathematical Systems Theory, Springer, New York, NY. Zbl0940.93002
- Pommaret J.F. and Quadrat A. (1998). Generalized Bézout identity, Applicable Algebra in Engineering, Communication and Computing 9(2): 91-116. Zbl1073.93516
- Pommaret J.F. and Quadrat A. (1999). Algebraic analysis of linear multidimensional control systems, IMA Journal of Mathematical Control and Information 16(3): 275-297. Zbl1158.93319
- 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 Optimization 45(6): 2035-2053. Zbl1126.93011
- Rapisarda P. and Willems J.C. (1997). State maps for linear systems, SIAM Journal on Control and Optimization 35(3): 1053-1091. Zbl0884.93006
- Rocha P. (1990). Structure and representation of 2-D systems, Ph. D. thesis, University of Groningen.
- Rocha P. and Wood J. (1997). A new perspective on controllability properties for dynamical systems, International Journal of Applied Mathematics and Computer Science 7(4): 869-879. Zbl0908.93011
- Shankar S. (2002). The evolution of the concept of controllability, Mathematical and Computer Modelling of Dynamical Systems 8(4): 397-406. Zbl1043.93008
- Valcher M.E. and Willems J.C. (1999). Observer synthesis in the behavioral approach, IEEE Transactions on Automatic Control 44(12): 2297-2307. Zbl1136.93340
- Willems J.C. (1986/87). From time series to linear system. Part I: Automatica 22: 561-580, Part II: Automatica 22: 675-694, Part III: Automatica 23: 87-115. Zbl0604.62090
- Willems J.C. (1991). Paradigms and puzzles in the theory of dynamical systems, IEEE Transactions of Automatic Control 36(3): 259-294. Zbl0737.93004
- Willems J.C. and Yamamoto Y. (2007). Representations of linear time-invariant behaviors by rational functions, Linear Algebra and its Applications 425(2-3): 226-241. Zbl1123.93011
- Wood J., Rogers E. and Owens D.H. (1999). Controllable and autonomous nD linear systems, Multidimensional Systems and Signal Processing 10(1): 33-69. Zbl0920.93023
- Wood J. (2000). Modules and behaviours in nD systems theory, Multidimensional Systems and Signal Processing 11(1-2): 11-48. Zbl0963.93015
- Zerz E. (2000). Topics in Multidimensional Linear Systems Theory, Springer, London. Zbl1002.93002
- Zerz E. (2006). An algebraic analysis approach to linear timevarying systems, IMA Journal of Mathematical Control and Information 23(1): 113-126. Zbl1106.93019
- Zerz E. (2007). Autonomy properties of multidimensional linear systems over rings, Proceedings of the 5th International Workshop on Multidimensional Systems (NDS 2007), Aveiro, Portugal. Zbl1142.93018

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