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Fluidification is a classical relaxation technique for approximated performance evaluation of discrete systems. In this paper we deal with T-timed fully continuous Petri Nets working under infinite servers semantics, what leads to (deterministic) piecewise linear differential systems. Switches among dynamic linear systems are triggered by internal events through minimum operators on marking variables. The observability problem consists of estimating the (initial) marking from a partial measure. This paper is devoted to observability concepts and criteria in this particular class of systems, not to the observers design. The concept of structural observability, regarding to the possibility of estimating the marking of places for any speed of the transitions is introduced and studied for the subclass of join-free Petri nets (JF). For non join-free Petri nets, conditions to compute suitable estimates will be established.