Mean square stability criteria for stochastic feedback systems

1 July 1973

journal article
research article
Published by Taylor & Francis in International Journal of Systems Science

Vol. 4 (4) , 545-564
https://doi.org/10.1080/00207727308920036

Abstract

In this paper several stability criteria are obtained for a class of stochastic feedback systems containing a multiplicative white noise element ; continuous time as well as discrete time systems are dealt with. Mean square stability properties are derived by means of Lyapunov theory ; the Lyapunov functions are generated by means of the Lyapunov equation, the path integral technique, and the Kalman-Yacoboviteh lemma. Results similar to the Routh-Hurtwitz conditions and the circle criteria for deterministic feedback systems are discussed. Different interpretations of the white noise element (Itò, Stratonovitch, etc.) are considered.

Keywords

This publication has 11 references indexed in Scilit:

Frequency domain stability criteria for stochastic systems
IEEE Transactions on Automatic Control, 1971
The Analysis of Feedback Systems
Published by MIT Press ,1971
On the stability of linear stochastic systems
IEEE Transactions on Automatic Control, 1969
A survey of stability of stochastic systems
Automatica, 1969
A New Representation for Stochastic Integrals and Equations
SIAM Journal on Control, 1966
Liapunov criteria for weak stochastic stability
Journal of Differential Equations, 1966
On the stabilization of unstable linear systems by white noise coefficient variations
Archive of Applied Mechanics, 1966
Linear Systems with Stochastic Coefficients†
International Journal of Control, 1965
A Frequency-Domain Condition for the Stability of Feedback Systems Containing a Single Time-Varying Nonlinear Element
Bell System Technical Journal, 1964
LYAPUNOV FUNCTIONS FOR THE PROBLEM OF LUR'E IN AUTOMATIC CONTROL
Proceedings of the National Academy of Sciences, 1963