Distributed stabilisation of spatially invariant systems: positive polynomial approach

0382623 - ÚTIA 2013 RIV US eng J - Journal Article
Augusta, Petr - Hurák, Z.
Distributed stabilisation of spatially invariant systems: positive polynomial approach.
Multidimensional Systems and Signal Processing. Roč. 24, Č. 1 (2013), s. 3-21. ISSN 0923-6082. E-ISSN 1573-0824
R&D Projects: GA MŠMT(CZ) 1M0567
Institutional research plan: CEZ:AV0Z10750506
Institutional support: RVO:67985556
Keywords : Multidimensional systems * Algebraic approach * Control design * Positiveness
Subject RIV: BC - Control Systems Theory
Impact factor: 1.578, year: 2013
http://library.utia.cas.cz/separaty/2013/TR/augusta-0382623.pdf

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.
Permanent Link: http://hdl.handle.net/11104/0212792