Bibliography

(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.