Theory of Stochastic Linear Systems with Gaussian Parameter Variations
作者:
J. Clifton Samuels,
期刊:
The Journal of the Acoustical Society of America
(AIP Available online 1961)
卷期:
Volume 33,
issue 12
页码: 1782-1786
ISSN:0001-4966
年代: 1961
DOI:10.1121/1.1908574
出版商: Acoustical Society of America
数据来源: AIP
摘要:
A theory of linear systems with randomly varying parameters is developed under the assumption that the parameter processes are Gaussian processes obtained by linear filtering of white noise. By this device, the restriction to white‐noise parameter processes of previous studies has been removed.By a method related somewhat to a technique used in the theory of the multiple scattering of light, a system of linear integral equations for the determination of various second‐order moments of the system output is derived. This system can be solved explicitly in some interesting cases.A theory of stability in mean and in mean square is given for random systems. It was found that mean square stability depended only on the values of the auto‐ and cross‐correlation functions of the parameter processes at the origin and not on the detailed structure of these functions.The stability theory is applied to an RLC circuit with randomly varying capacitance. The possibility of stabalizing unstable deterministic systems with random noise is discussed.
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