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This paper is concerned with the problem of stability of linear and nonlinear interconnected systems having white noise parameter variations. It is shown that the stochastic version of the Liapunov's second method may be successfully utilized in order to develop an aggregation and decomposition theory for the concerned systems. This, in turn, permits derivation of relatively simple decentralised criteria for the stability of the composite systems

The paper presents a method for generating a scalar Liapunov function for the multimachine power system by employing a simple aggregation technique. It is shown that the proposed technique allows decomposition of an N machine system into N-1 subsystems for which simple Popov type stability conditions are estabilshed. The results are illustrated by considering a 3 machine system. It is shown that the criteria developed in the paper yields much larger regions of stability.