Abstract
A general theory of mean square stability of random linear systems is developed when several system parameters vary as white noise stochastic processes. It is found that stability in mean square is determined from the character of the roots of a determinantal equation involving the Fourier transforms of double products of the weighting functions of the “average” system and the spectral densities of the parameter processes. The general theory is applied to the mean square stability of an RLC circuit in which the resistance and capacitance have purely random fluctuations. In the course of the study, a new type of dynamic stability is predicted, namely, the possibility of stabilizing unstable deterministic systems with random noise. Preliminary experimental studies appear to confirm this theoretical prediction.
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