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 hybrid systems simulate Turing machines, this immediately shows these classes are undecidable. We discuss the observability of piecewise-affine hybrid systems, and give a number of examples illustrating different observability propertie