Stability Analysis for Spatially Distributed Dynamic Systems

In this paper, a sufficient condition is derived for the stability of a spatially invariant distributed dynamical (SIDD) system, based on the geometrical structure of the null space of a matrix polynomial. This condition is less conservative than the available computationally feasible criteria. Moreover, using the idea of parameter dependent linear matrix inequalities (LMI), a necessary and sufficient condition is obtained. Both of these two conditions are expressed by LMIs, and can therefore in principle be computationally verified. While the necessity of the latter condition is lost if the degree of the related multivariate matrix polynomials is small, its conservatism can be sequentially reduced through increasing this degree step by step.