In this note, moment stability of nonlinear stochastic systems with time-delays is investigated. Based on a kind of Kronecker algebra and the H-representation technique, we obtain the second order moment equations of nonlinear stochastic systems with time-delays. By the comparison principle and the established moment equations, we get the comparative systems of the nonlinear stochastic systems with time-delays. Then we establish moment stability theorems for the systems with the stability properties of the comparative systems. Finally, an example is presented to illustrate the efficiency of our results.

Moment Stability of Nonlinear Stochastic Systems With Time-Delays Based on ${\cal {H}}$ -Representation Technique

Mean square stability of a second-order parametric linear system excited by a colored Gaussian noise

The asymptotic stochastic stability in large of the composite stochastic systems

Moment stability for linear systems with a random parametric excitation

This paper is concerned with investigating the p th moment asymptotic stability of linear systems subject to non-Gaussian multiplicative (state-dependent) noise. The noise processes are a form of filtered Poisson processes. A technique is presented for investigating the pth moment asymptotic stability of linear systems satisfying certain Lie algebraic conditions. Several examples are presented to illustrate the technique.

Stochastic stability for a class of systems with multiplicative state noise

In this paper a particular class of linear parametric stochastic systems is considered. For this class the moment stability problem is analysed: it is shown that the stability conditions do not depend on the noise bandwidth. An equivalent Ito equation is derived. Explicit criteria for the stability of the moments, for pth mean stability and for almost sure stability are obtained.

J. L. Willems

Papers

An equivalence result for moment stability criteria for parametric stochastic systems and ltd equations