Some remarks concerning the stability of a linear stochastic system

• Published in: Journal of applied mathematics and mechanics 1966, Vol.30 (6), p.1332-1335
• Main Author: Nevel'son, M.B.
• Format: Article
• Language: English
• ISSN: 0021-8928; 0021-8928
• DOI: 10.1016/0021-8928(66)90099-2

The method for investigating the asymptotic stability in the mean square of a linear stochastic system with Gaussian “white noises” proposed in [1] is developed. Section 1 contains an interpretation of the result obtained [1] in terms of the stability quality criterion employed in controlled systems theory. Section 2 contains the necessary and sufficient conditions of asymptotic stability in the mean square in the Routh-Hurwitz form of a linear stochastic system for the case where the intensities of noises acting in different directions are proportional to each other. This result generalizes the stability conditions given in [1 and 2] ∗ ∗ We take this opportunity to note that [1] contains the following misprints which make its reading difficult. In the right-hand side of Formula (2.5) on p. 406, the exponent of λ ought to contain the number 2. On p.407. fourth line from top, one should read (−1) j−1 λ i+ j−2 instead of (−1) i+ j−1 λ i−2 .