Finite Abstractions of Network of Impulsive Systems Using Dissipativity Approach

This paper introduces a compositional framework for constructing finite abstractions of nonlinear interconnected impulsive systems using dissipativity-based conditions. Central to our approach is the concept of “alternating simulation functions,” which serve to relate the concrete dynamics of impulsive subsystems to their finite abstractions. Dissipativity conditions are employed to ensure the compositionality of the finite abstractions, enabling the representation of complex interconnected systems as compositions of their subsystem abstractions. The methodology relies on incremental passivity properties such as supply rates and storage functions, alongside forward completeness, to construct finite abstractions for individual impulsive subsystems.