| In this paper, first we review the general methods of analysis of stability of large-scale systems, and in particular, we discuss scalar Lyapunov approach and vector Lyapunov approach by using linear time-varying system as example. Then we present an introduction about partial decomposing approach of stability analysis by using linear time-varying system as an example. Finally, in the main part of this paper, we consider the stability problem for linear, time-delay large-scale systems and nonlinear large-scale systems with strong coupling in single direction among subsystems. Partial decomposing approachs of stability analysis for time-delay large-scale system and non-linear large-scale system are proposed. By using this approach, large-scale systems with strong coupling in single direction can be decomposed into some decoupling subsystems in a single direction. Using Lyapunov functional and linear matrix inequality (LMI) technique, and through the stability of subsystems decoupled in a single direction, we obtain an estimation formula of parameter's stability domain. These two approaches can significantly simplify the computing work for stability analysis.In the theory of stability for large-scale systems there are mainly two kinds of analysis approaches. Including the scalar Lyapunov approach and the vector Lyapunov approach. The two approaches are generally suitable for the large-scale system with weak coupling among subsystems. When it comes to the stability analysis of large-scale systems, there have been some researchresults. However most of these results have been focused on large-scale system with weak coupling, and little attention has been paid to large-scale systems with strong coupling. The main contribution of this paper is the presentation of partial decomposing approach of stability analysis for time-delay large-scale system and non-linear large-scale system with strong coupling in single direction.
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