Discrete state observability of hybrid systems

We propose a novel definition of observability, motivated by safety critical applications, given with respect to a subset of critical discrete states that model unsafe or unallowed behaviors. For the class of discrete event systems, we address the problem in the setting of formal (regular) languages and propose a novel observability verification algorithm. For the class of switching systems, we characterize the minimal set of extra output information to be provided by the continuous signals in order to satisfy observability conditions, and propose a milder observability notion that allows a bounded delay in state observation. For the class of hidden Markov models, we analyze decidability and complexity of the verification problem