0347862 20240111140744.920101011235959.9 7 s. DVD Rom cav_un_epca*0347861978-963-311-370-7773-779BudapestEötvös Loránd University2010 polynomial matrix boundary control differential equations 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 textový dokument 463 kB 1M0567 GA MŠk CZ cav_un_auth*0202350 CEZ:AV0Z10750506 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. cav_un_auth*0264563 The 19th International Symposium on Mathematical Theory of Networks and Systems - MTNS 2010 Budapešť 05.07.2010-09.07.2010 HU 2011 BC 2 http://hdl.handle.net/11104/0188540 2010 textový dokument 463 kB cav_un_epca*0347861 Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems - MTNS 2010 978-963-311-370-7 773 779 Budapest Eötvös Loránd University 2010