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Distributed stabilisation of spatially invariant systems: positive polynomial approach
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SYSNO ASEP 0382623 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Distributed stabilisation of spatially invariant systems: positive polynomial approach Author(s) Augusta, Petr (UTIA-B) RID
Hurák, Z. (CZ)Number of authors 2 Source Title Multidimensional Systems and Signal Processing. - : Springer - ISSN 0923-6082
Roč. 24, Č. 1 (2013), s. 3-21Number of pages 19 s. Language eng - English Country US - United States Keywords Multidimensional systems ; Algebraic approach ; Control design ; Positiveness Subject RIV BC - Control Systems Theory R&D Projects 1M0567 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) Institutional support UTIA-B - RVO:67985556 CEZ AV0Z10750506 - UTIA-B (2005-2011) UT WOS 000312715000002 EID SCOPUS 84871789562 DOI 10.1007/s11045-011-0152-5 Annotation The paper gives a computationally feasible characterisation of spatially distributed controllers stabilising a linear spatially invariant system, that is, a system described by linear partial differential equations with coefficients independent on time and location. With one spatial and one temporal variable such a system can be modelled by 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 bi-variate polynomial c. The paper is built on the relationship between 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. For low-order discrete-time systems it is shown that a linearising factorisation of the polynomial Schur-Cohn matrix exists. For higher order plants and/or controllers such factorisation is not possible as the solution set is non-convex and one has to resort to some relaxation. For continuous-time systems, an analogue factorisation of the polynomial Hermite-Fujiwara matrix is not known. Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2013
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