0382623 20240103201432.920121107235959.9 000312715000002 84871789562 10.1007/s11045-011-0152-5 19 s. cav_un_epca*02572860923-6082243-21Springer Multidimensional systems Algebraic approach Control design Positiveness cav_un_auth*0213204 Augusta Petr Teorie řízení Department of Control Theory TŘ TR UTIA-B Department of Control Theory Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0021097 Hurák Z. CZ http://library.utia.cas.cz/separaty/2013/TR/augusta-0382623.pdf http://dx.doi.org/10.1007/s11045-011-0152-5 1M0567 GA MŠk CZ cav_un_auth*0202350 CEZ:AV0Z10750506 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. 2013 BC 2 4 A 4a 20231122135256.9 RVO:67985556 http://hdl.handle.net/11104/0212792 COMPUTERSCIENCETHEORYMETHODS|ENGINEERINGELECTRICALELECTRONIC 1.420 0.400 6.V 0.00096 0.512 355 35 0.810 ScienceCitationIndex Q1 46.217 69.341 Q3 Q2 2013 Soubory v repozitáři: augusta-0382623.pdf 84871789562 SCOPUS 000312715000002 WOS cav_un_epca*0257286 Multidimensional Systems and Signal Processing 0923-6082 1573-0824 Roč. 24 Č. 1 2013 3 21 Springer