A new concept of fair diagnosability in hybrid dynamical systems

Failure detection and diagnosis is an important paradigm in automatic control of complex systems. Study of failure diagnosability of discrete event systems has been widely carried out and is reported in the literature. It is commonly held that failures resulting from permanent faults can be diagnosed by ignoring the continuous dynamics of the hybrid systems. The present paper demonstrates that the fairness property of the transitions due to the underlying continuous dynamics plays an important role in deciding about the diagnosability of the system. Accordingly, discrete modeling of hybrid systems ignoring the continuous dynamics impairs the diagnosability of failures caused by even permanent failures. This inadequacy is first illustrated through an example. A new diagnosability condition has been proposed next and illustrated through the same example.