Observability and extendability of finite support nD behaviors

In this contribution the local structure of finite support nD signals is analysed according to the behavioral approach. Observability and local detectability are introduced, and characterized in terms of polynomial matrix descriptions. The problem of extending into a legal trajectory a set of data that satisfies the parity checks on a suitable subset of Zⁿ is then considered and necessary and sufficient conditions for its solution provided. The main properties of locally undetectable behaviors and their connections with the notion of constrained variables are investigated. A general representation result for finite support behaviors is finally discussed