Observability of hybrid systems and turing machines

In this paper we discuss the observability of hybrid systems and turing machines. We give an elementary example to show that observability is undecidable for turing machines with output. Since many classes of system simulate turing machines, we can then show that observability for these classes is undecidable. We discuss the observability of piecewise-affine hybrid systems, and give examples illustrating different observability properties.