Abstract
In this paper we study linear discrete two-dimensional systems in the behavioral context where control is viewed as interconnection. Within the behavioral framework a natural concept of interconnection has been introduced by J.C.Willems, called regular interconnection. We investigate regular interconnections that yield finite dimensional behaviors, and prove that when a finite dimensional behavior can be achieved from a given behavior \(\text{\usefont{U}{euf}{m}{n}B}\) by regular full/partial interconnection then the controllable part/manifest part of \(\text{\usefont{U}{euf}{m}{n}B}\) is rectifiable.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Belur, M.N., Trentelman, H.L.: Stabilization, pole placement, and regular implementability. IEEE Trans. Automat. Control 47(5), 735–744 (2002)
Bisiacco, M., Valcher, M.E.: Two-dimensional behavior decompositions with finite-dimensional intersection: a complete characterization. Multidimens. Syst. Signal Process 16(3), 335–354 (2005)
Julius, A.A., Willems, J.C., Belur, M.N., Trentelman, H.L.: The canonical controllers and regular interconnection. Systems & Control Letters 54(8), 787–797 (2005)
Napp Avelli, D.: Almost direct sum decomposition and implementation of \(2\textrm{D}\) behaviors. Math. Control Signals Systems 21(1), 1–19 (2009)
Oberst, U.: Almost regular interconnection of multidimensional behaviors. Accepted for publication in SIAM Journal on Control and Optimization (2008)
Pillai, H., Shankar, S.: A behavioral approach to control of distributed systems. SIAM J. Control Optim. 37(2), 388–408 (1998)
Rocha, P.: Feedback control of multidimensional behaviors. Systems & Control Letters 45, 207–215 (2002)
Rocha, P.: Canonical controllers and regular implementation of nD behaviors. In: Proceedings of the 16th IFAC World Congress, Prague, Chech Republic (2005)
Rocha, P.: Stabilization of multidimensional behaviors. Multidimens. Systems Signal Process 19, 273–286 (2008)
Rocha, P., Wood, J.: Trajectory control and interconnection of 1D and nD systems. SIAM J. Control Optim. 40(1), 107–134 (2001)
Trentelman, H.L., Napp Avelli, D.: On the regular implementability of nD systems. Systems and Control Letters 56(4), 265–271 (2007)
Willems, J.C.: On interconnections, control, and feedback. IEEE Trans. Automat. Control 42(3), 326–339 (1997)
Zerz, E.: Primeness of multivariate polynomial matrices. Systems Control Lett. 29(3), 139–145 (1996)
Zerz, E.: Multidimensional behaviours: an algebraic approach to control theory for (PDE). International Journal of Control 77(9), 812–820 (2004)
Zerz, E., Lomadze, V.: A constructive solution to interconnection and decomposition problems with multidimensional behaviors. SIAM J. Control Optim. 40(4), 1072–1086 (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Napp Avelli, D., Rocha, P. (2009). Implementation of 2D Strongly Autonomous Behaviors by Full and Partial Interconnections. In: Bru, R., Romero-Vivó, S. (eds) Positive Systems. Lecture Notes in Control and Information Sciences, vol 389. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02894-6_36
Download citation
DOI: https://doi.org/10.1007/978-3-642-02894-6_36
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02893-9
Online ISBN: 978-3-642-02894-6
eBook Packages: EngineeringEngineering (R0)