On the 2nd Moment Stability of Stochastic Linear Systems

概要

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Linear systems with randomly time varying parameters which are stationary stochastic process (stationary random process), have been investigated for many years by Rosenbloom, Samuels, Bertram, Bergen, Bershad and others.This paper is intended to extend the works by Rosenbloom and to develop the idea of Bershad. It is now considered that the linear systems are represented by generalized state equations using linear operator matrix. The system stability, in stochastic sense, is determined by examining whether or not the 2nd moments of the corresponding state variables are bounded. All of the random parameters are assumed to be Gaussian and non-white process. Two theorems of the 2nd moment stability are derived. Especially, latter theorem, relating to partially disturbed systems, gives a practical sufficient condition for the stochastic stability of such a system. Simple illustrative examples are also presented.
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