2016/01/06 by Mario Sassano, Luca Zaccarian, Sassano, Mario +1
Engineering · #Advanced Control Systems Optimization #FOS: Electrical engineering #Stability and Control of Uncertain Systems #Stability and Controllability of Differential Equations #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1601.01271
openalex publication_date 2016/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this short note we prove a hierarchical stability result that applies to hybrid dynamical systems satisfying the hybrid basic conditions of (Goebel et al., 2012). In particular, we establish sufficient conditions for uniform asymptotic stability of a compact set based on some hierarchical stability assumptions involving two nested closed sets containing such a compact set. Moreover, mimicking the well known result for cascaded systems, we prove that the basin of attraction of such compact set coincides with the largest set from which all solutions are bounded. The result appears to be useful when applied to several recent works involving hierarchical control architectures.