Abstract
The purpose of this paper is to present a unified treatment on controllability/observability problems for distributed parameter systems, and give its applications in distributed parameter control theory. For this purpose, from a basic weighted identity of parabolic-like partial differential operator (i.e., without elliptic condition), we will give all the known controllability/observability results for the parabolic, hyperbolic, Schrodinger and plate equations that are derived via Carleman estimate. Meanwhile, based on this weighted identity, we also give its applications in the stabilization of hyperbolic equations and the controllability/observability for the complex Ginzburg-Landau equations, etc.
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