Work

Compositional Construction of Approximately Bisimilar Symbolic Models for Discrete-Time Interconnected Switched Linear Systems

Year: 2026

Type: article

Abstract: Symbolic models based on approximate bisimulation are key to formal verification and control synthesis, as they make complex temporal logic tasks for dynamic systems computationally feasible. A major challenge in constructing such models—especially with grid-based methods—is the “curse of dimensionality,” which severely limits scalability for large-scale systems. Compositional symbolic model solves this problem by first building symbolic models for individual components and then integrating them into a global model. However, existing compositional methods only apply to a narrow class of discrete-time interconnected switched systems (DT-ISS). They require all subsystems in component switched systems (CSS) to be incrementally input-state stable. Notably, these methods are not applicable to practical DT-ISS with unstable subsystems, thus forming a critical research gap. Hence, this paper proposes a new compositional method that removes the stability requirement for CSS subsystems, thereby filling the aforementioned research gap. A grid-based approach generates symbolic models for each CSS (even those with non-stable subsystems), which are then interconnected to form the global symbolic model of the DT-ISS. Using mode-dependent dwell time constraints and discrete Lyapunov techniques, we derive tractable existence conditions for the bisimulation function between each CSS and its symbolic model in the form of linear matrix inequalities (LMIs). These functions are then used to derive the bisimulation function between the DT-ISS and its global symbolic model. Two simulation examples are given to demonstrate our method has a much broader application scope than existing approaches.

Source: IEEE Access

DOI: 10.1109/access.2026.3651451

Authors: Yang Song, Yongzhuang Liu, Wanqing Zhao

Institutions: Shanghai University, Taishan University, Newcastle University

Language: English

Topic: Formal Methods in Verification

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,075

Funders: National Natural Science Foundation of China, Higher Education Discipline Innovation Project