ABSTRACT
In the theory of the motion stability of systems with random structure the problem of Lyapunov function construction is of topical interest. With the framework of the development of decomposition methods for systems with random structure there arose the possibility of applying Lyapunov functions consisting of more than one component. Nowadays the technique is used for two types of multicomponent function, namely, vector- and matrix-valued functions. In some cases both vector- and matrix-valued functions help to simplify the construction of auxiliary Lyapunov functions. This, in its turn, opens up new possibilities for the application of the direct Lyapunov method to stability investigation of systems with random structure.
