# Bibliography

Conference Paper (international conference)

### Distributed stabilization of spatially invariant systems: positive polynomial approach

,

**: **Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems - MTNS 2010, p. 773-779

**: **The 19th International Symposium on Mathematical Theory of Networks and Systems - MTNS 2010,
(Budapešť, HU, 05.07.2010-09.07.2010)

**: ** CEZ:AV0Z10750506

**: **1M0567, GA MŠk

**: **polynomial matrix,
boundary control,
differential equations

**(eng): **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.

**: **BC