Decomposition and Stability Analysis for Complex Systems with Dynamic Interconnections

Abstract

A method to decompose dynamic complex systems is proposed, that is, by using the dynamic inclusion principle and permutation transformation, complex system with information constrains of dynamic topology structure is decomposed as a group of pair-wise decoupled subsystems in the expanded space. Then according to the Lyapunov method, the connective stability of pair-wise subsystems is discussed by constructing Lyapunov functions in the case all isolated systems are stable, the conditions of connective stability for the expanded system are obtained, which are also adapt to the original system based on inclusion principle. Finally, the theorem and deduction of connective stability for the dynamic interconnnected complex system are given.