Observability analysis and observer design for finite automata via matrix approach

This study investigates the observability problem and the observer design of partially observed finite automata via a matrix approach. Using semi-tensor product of matrices, finite automata are modelled in the form of discrete-time bilinear systems. Matrix-form necessary and sufficient conditions for both the initial and current state observability, either with or without input information, are first proposed. Based on that, a constructive method for the observer design is provided.