Symbolic Models for Interconnected Impulsive Systems

In this paper, we present a compositional method-ology for constructing symbolic models of nonlinear interconnected impulsive systems. Our approach relies on the concept of “alternating simulation function” to establish a relation-ship between concrete subsystems and their symbolic models. Assuming some small-gain type conditions, we develop an alternating simulation function between the symbolic models of individual subsystems and those of the nonlinear interconnected impulsive systems. To construct symbolic models of nonlinear impulsive subsystems, we propose an approach that depends on incremental input-to-state stability and forward completeness properties. Finally, we demonstrate the advantages of our framework through a case study.