Stability analysis of numerical methods for ordinary differential equations (ODEs) is motivated by the question “for what choices of stepsize does the numerical method reproduce the characteristics of the test equation?” We study a linear test equation with a multiplicative noise term, and consider mean-square and asymptotic stability of a stochastic version of the theta method. We extend some ...

This paper studies the stability of Kalman filtering over a network subject to random packet losses, which aremodeled by a time-homogeneous ergodicMarkov process. For second-order systems, necessary and sufficient conditions for stability of the mean estimation error covariance matrices are derived by taking into account the system structure. While for certain classes of higher-order systems, n...

In this paper, we investigate the problem of stability time-varying stochastic perturbed singular systems by using Lyapunov techniques under assumption that initial conditions are consistent. Sufficient on uniform exponential and practical in mean square solutions obtained based upon techniques. Furthermore, study stabilization some classes systems. Finally, provide numerical examples to valida...