Stability Analysis for a Class Pseudo-Linear Complex Systems

Abstract

Based on inclusion principle, M-matrices theory and Lyapunov stability theory, the connective stability of a class pseudo-linear complex systems was discussed. Firstly, by using the inclusion principle and permutation transformation, the system is decomposed as a recurrent reverse order of pair-wise subsystems in the expanded space. Then, the Lyapunov functions of all isolated subsystems are constructed to ensure them stable, on this basis, the connective stability of pair-wise subsystems and the expanded system are analyzed, and the connectively stable conditions of the expanded system are obtained. In the frame of inclusion principle, the connectively stable conditions of the expanded system are also adapt to the original system. Finally, the theorem on stability of the pseudo-linear complex systems is given.