Hierarchical stability of nonlinear hybrid systems
Provides a theoretical stability result for hybrid systems with hierarchical control architectures, but is incremental as it extends known cascaded system results.
The paper proves sufficient conditions for uniform asymptotic stability of a compact set in nonlinear hybrid systems using hierarchical stability assumptions, and shows that the basin of attraction equals the largest set with bounded solutions.
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.