Approximately Bi-similar Symbolic Model for Discrete-time Interconnected Switched Linear System

The approximately bi-similar symbolic model of control system is the foundation for addressing temporal logic tasks. This paper concerns the construction of approximately bi-similar symbolic models for discrete-time interconnected switching systems (DT-ISS). Considered discrete-time impulsive switched system (DT-ISS) comprises interconnected component switched systems (CSS). While some literatures have investigated the construction of approximately bi-similar symbolic models for DT-ISS, existing approaches presuppose incrementally input-state stable for all CSS subsystems. This paper relaxes the stability assumptions on subsystems, investigates a more general class of DT-ISS, and studies the compositional construction of approximately bi-similar symbolic models for such systems. Firstly, a grid method is used to construct component symbolic models (CSMs) for CSS, then obtained the DT-ISS symbolic model through interconnection of component abstractions. Secondly, the component bi-simulation functions are derived through linear matrix inequalities (LMIs), and the bi-simulation functions between the DT-ISS and its symbolic model are then constructed using the combination construction method. Meanwhile sufficient conditions for their existence are provided. Finally, the effectiveness of the proposed results is validated through a study of the case traffic network.