Detectability of mix-valued logical control networks based on a Luenberger-like observer approach

This research investigates detectability of a class of mix-valued logical control networks through the application of a Luenberger-like observer. First, three concepts of detectability: detectability, strong detectability, and weak detectability are defined for the mix-valued logical control networks. Subsequently, the equivalent algebraic form of the control networks is obtained to deal with the three kinds of detectability. A Luenberger-like observer for the equivalent algebraic representation is designed to tackle the challenges. Then some necessary and sufficient conditions for detectability are derived by employing the observer associated with detecting the states of the control networks. Finally, two examples are presented to effectively demonstrate our obtained conclusions in both theory and applications. Moreover it is shown that our proposed observer scheme has good performance.