Distributed stabilisation of spatially invariant systems via positive polynomial approach: MIMO systems case

The linear spatially-distributed time-invariant systems with multiple inputs and multiple outputs, modelled by the bivariate transfer function are considered. Stabilisation technique is based on the relationship between stability of the closed-loop bivariate polynomial and positiveness of a related polynomial matrix on the unit circle. Since such matrix is not linear in coefficients of the original polynomial and cannot be used for controller design directly, a linearising factorisation is found. This concept is applied to a system with multiple outputs - a heat conduction in a long thin metal rod equipped with an array of temperature sensors and heaters, where heaters are placed in larger distances than sensors.