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Distributed stabilization of spatially invariant systems: positive polynomial approach
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SYSNO ASEP 0347862 Document Type C - Proceedings Paper (int. conf.) R&D Document Type Conference Paper Title Distributed stabilization of spatially invariant systems: positive polynomial approach Author(s) Augusta, Petr (UTIA-B) RID
Hurák, Z. (CZ)Number of authors 2 Source Title Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems - MTNS 2010. - Budapest : Eötvös Loránd University, 2010 - ISBN 978-963-311-370-7 Pages s. 773-779 Number of pages 7 s. Publication form DVD Rom - DVD Rom Action The 19th International Symposium on Mathematical Theory of Networks and Systems - MTNS 2010 Event date 05.07.2010-09.07.2010 VEvent location Budapešť Country HU - Hungary Event type WRD Language eng - English Country HU - Hungary Keywords polynomial matrix ; boundary control ; differential equations Subject RIV BC - Control Systems Theory R&D Projects 1M0567 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) CEZ AV0Z10750506 - UTIA-B (2005-2011) Annotation The paper gives a computationally feasible characterisation of spatially distributed discrete-time controllers stabilising a spatially invariant system. This gives a building block for convex optimisation based control design for these systems. Mathematically, such systems are described by partial differential equations with coefficients independent on time and location. In this paper, a situation with one spatial and one temporal variable is considered. Models of such systems can take a form of a 2-D transfer function. Stabilising distributed feedback controllers are then parametrised as a solution to the Diophantine equation ax + by = c for a given stable bivariate polynomial c. This paper brings a computational characterisation of all such stable 2-D polynomials exploiting the relationship between a stability of a 2-D polynomial and positiveness of a related polynomial matrix on the unit circle. Such matrices are usually bilinear in the coefficients of the original polynomials. Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2011
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