A constructive approach for the observability of coupled linear systems

We present a constructive method for the study of observability or partial observability of weakly coupled linear distributed systems or, more generally, of compactly perturbed systems. This approach allows us to avoid the usual indirect compactness–uniqueness arguments in many cases. It is based on two ideas: a detailed study of the dependence of some constants on the initial data and on a generalization of an estimation method of A. Haraux in nonharmonic analysis.