The distinguishability of linear control systems

When observabilities of hybrid systems such as piecewise-affine hybrid systems are considered, the distinguishability of subsystems takes a very important role. However, properties and even definitions of such distinguishabilities have not been extensively studied in the literature. This paper will give a definition of the distinguishability of two linear control systems and present the necessary and sufficient condition of the distinguishability, giving an answer for the problem posed by Vidal et al.