Modeling and stability analysis of state-switched hybrid systems via Differential Petri Nets

State-switched systems are a large class of hybrid systems with numerous applications. In this work, the representation of state-switched systems in a Differential Petri Net (DPN) formalism becomes possible through a novel transformation of the fundamental equation of the DPN model into a form compatible with state-switching. Furthermore, we use the approach of the switching hyperplanes to provide means for the stability analysis of state-switched systems in a DPN framework. We also investigate stability issues of the resulting DPNs and synthesize an algorithm that can determine the stability of the state-switched DPN. Stability conditions are also expressed as Linear Matrix Inequalities (LMI) so that they can be easily determined using commercial software.