Stability of One-Dimensional Spatially Invariant Arrays Perturbed by White Noise

For the one-dimensional spatially invariant array, a necessary and sufficient stability condition in terms of the Schur stability of a matrix over spatial frequency is obtained in this paper Then based on the theorem on nonnegative pseudo-polynomial matrices, the frequency-dependent stability condition is converted to a finite dimensional linear matrix inequality (LMI) problem, the solution of which is easy to compute