Extension beyond tree graphs and continuous-time implementation

Establish analogous convergence guarantees for the intrinsic signum–gradient protocol on general connected graphs and for sampled-data implementations of the protocol.

Background

The main results rely on the tree topology, particularly the lower bound obtained by contracting zero-error clusters and identifying leaf clusters. The paper also analyzes an ideal continuous-time Filippov protocol, while its numerical illustrations use a discretization and tolerances rather than establishing sampled-data guarantees. The conclusion explicitly identifies both general graph topologies and sampled-data implementations as unresolved directions.