Approximately Bi-Similar Symbolic Model for Discrete-Time Interconnected Switched System

Dear Editor, This letter concerns the development of approximately bi-similar symbolic models for a discrete-time interconnected switched system (DT-ISS). The DT-ISS under consideration is formed by connecting multiple switched systems known as component switched systems (CSSs). Although the problem of constructing approximately bi-similar symbolic models for DT-ISS has been addressed in some literature, the previous works have relied on the assumption that all the subsystems of CSSs are incrementally input-state stable. By removing this stability assumption on subsystems, this letter considers a more general DT-ISS and studies the compositional construction of the approximately bi-similar symbolic model of such DT-ISS. To achieve this, firstly, the component symbolic models (CSMs) of CSSs are constructed using the grid method. Additionally, the component bi-simulation functions between them are established, and sufficient conditions for their existence are provided. Next, a compositional construction approach is applied to interconnect the CSMs of the CSSs, resulting in the symbolic model of the DT-ISS. Moreover, the bi-simulation functions between the DT-ISS and its symbolic model are presented, along with sufficient conditions for their existence. Finally, a simulation example is presented to verify the conclusions.