THE GLOBAL STABILITY ANALYSIS OF NONLINEAR LARGE SCALE INTERCONNECTED SYSTEMS

In this paper, an analytical approach for global asymptotic stability of a class of large scale interconnected systems is developed. Using the notations and properties of tensor algebra a global mathematical model is derived taking into account all the interconnections between the systems. Considering this model, the global stability analysis associated to a homogenous Lyapunov functions can be easily investigated. Sufficient conditions in terms of Lyapunov's direct method for large scale interconnected sytems are proposed to guarantee the global asymptotic stability. These conditions are presented as linear matrix inequalities (LMIs) feasibility tests. A numerical example is given to illustrate the results derived throughout the paper.