## Interconnected dynamical systems: stability, decomposition, and decentralisation |

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A-BK A-BKC aggregated flow analysis application approach arc i,j asymptotically stable basic solution blem block calculation co-ordination complex systems consider consistently ordered constraints convergence corresponds criteria criterion decentralised decider decomposition decomposition method defined destination determination diagonal differential inequality differential system distributed algorithm dual dual method dynamic eigenvalues example exists feasible Figure formulation Gauss-Seidel method global gradient graph hierarchical initial interactions iterative methods large scale systems Let us note linear programming linear systems loop Lyapunov equation Lyapunov functions Lyapunov method matrix minimal paths minimisation node non-linear obtained optimal control optimal solution oriented tree parameters partitioning perturbations polyhedron positive definite possible processors properties protocol resolution Riccati equation routing policy satisfied scalar sequential stabilising stability structure sub-problems sub-systems system of comparison theorem tion TITLI traffic variables