Abstract Stability of systems with random parametric excitation was investigated by several workers. The cases when the stability towards white-noise excitation was investigated were the most successfull ones, since the methods of the theory of Markov processes (see eg. [1 to 4] e.a.) could be utilised. Investigation of stability under nonwhite excitation is much harder, and this is the reason why most authors limited their investigations to either linear [5 to 7] or nonlinear systems of some particular type [7]. In [8] we find the stability criteria for an arbitrary nonlinear system with excitations of any type, but this criterion is effective only in the cases when the solution is a Markov process. Authors of [8 and 9] introduced the use of Liapunov function in problems of stability under random excitation. We shall however utilise that aspect of the Liapunov method, which was first used for similar purposes by the authors of [10 and 7].
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