Semi‐global edge‐consensus of linear discrete‐time multi‐agent systems with positive constraint and input saturation

Scale‐free collaborative protocols for global regulated state synchronization of discrete‐time homogeneous networks of non‐introspective agents in presence of input saturation

“…F I G U R E 2 Architecture of the linear collaborative protocol Theorem 3. Consider an MAS described by ( 3) with (37), and the associated exosystem (6). Let a set of nodes  be given which defines the set G N  .…”

“…Then, we choose matrix K = −𝜀B T PA, where 𝜀 ∈ (0, 𝜀 * ) with 𝜀 * = ||B T PB|| −1 , and P is a positive definite matrix satisfying (37). ζ i (k) and 𝜁 i (k) are defined by ( 23) and (10), respectively.…”

“…then we have the following closed-loop system 𝜎 T (u(j))(u(j) − 𝜎(u(j))), (40) where 𝜌 > 0 is a predesign parameter, P > 0 satisfies (37), and P D > 0 satisfies…”

“…where F is a design matrix such that A − FC is Schur stable. Then, we choose matrix K = −𝜀B T PA, where 𝜀 ∈ (0, 𝜀 * ) with 𝜀 * = ||B T PB|| −1 and P is a positive definite matrix satisfying (37). Meanwhile,…”

“…Then, global synchronization via static protocols for MAS with partial state coupling and linear general dynamics is developed for detailed balanced graph in Reference 36. The semi‐global result can be found in Reference 37 for undirected and strongly connected graph. So far, there is almost no result on global synchronization for discrete‐time MAS with linear general dynamics under directed graph only containing spanning tree.…”