Stable-protocol admissible synchronizability for high-order singular complex networks with switching topologies

Stable-protocol admissible synchronization analysis and design problems for singular complex networks with both connected switching topologies and jointly connected switching topologies are investigated. Firstly, a singular observer-type synchronization protocol is introduced, where the errors of protocol states among neighboring agents are applied to make complex networks satisfy a specific separation principle which can simplify synchronization analysis and design problems. Then, by the orthonormal projection operators between the synchronization subspace and the complement synchronization subspace, stable-protocol admissible synchronization problems are transformed into admissible ones of multiple subsystems with lower dimensions, and an approach is given to determine the synchronization function. Furthermore, stable-protocol admissible synchronizability criteria for connected switching topology cases and jointly connected switching topology cases are proposed, respectively. Finally, two numerical examples are given to demonstrate the effectiveness of theoretical results.