K-detectability in discrete event systems

This paper studies observability in discrete event systems (DES), and introduces and analyzes the property of K-detectability. In particular, a given DES is strongly K-detectable if eventually (after a finite number of observations) all corresponding sets of possible states (current state estimates following any given sequence of observations) are guaranteed to have cardinality less than or equal to K, where K is a positive integer. Note that for K = 1, strong K-detectability reduces to the standard notion of strong detectability. The paper briefly discusses ways to verify K-detectability using the standard observer construction (with exponential complexity) and also proposes a new construction (called the K-detector) that can be used to verify K-detectability with polynomial complexity.