Solution of the Problem of Constructing Liapunov Matrix Function for a Class of Large Scale Systems

New sufficient conditions for the Liapunov stability of a class of large scale systems described by ordinary differential equations are estab- lished. In all cases we proposed a new construction for matrix-valued Lia- punov function and the objective is the same: to analyze the stability of large scale systems (nonautonomous and autonomous) in terms of sign definiteness of specific matrices. In order to demonstrate the usefulness of the presented results several examples are considered.