In this paper, the problem of stability analysis for a class of impulsive stochastic fuzzy Cohen-Grossberg neural networks with mixed delays is considered. Based on M-matrix theory and stochastic analysis technique, a sufficient condition is obtained to ensure the existence, uniqueness, and global exponential stability in mean square means of the equilibrium point for the addressed impulsive st...

In this paper, we study the problem of stability analysis and controller synthesis of continuous-time linear networked systems in the presence of stochastic uncertainty. Stochastic uncertainty is assumed to enter multiplicatively in system dynamics through input and output channels of the plant. We used the mean square notion for stochastic stability to address the analysis and controller synth...

This paper considers the stability of moments of stochastic systems, such as stability of the mean or mean-square stability. The exponential growth behavior of moments is compared to almost sure exponential growth via Lyapunov exponents. We develop a series of indices that are useful to describe system performance under random perturbations. The theory is applied to two examples, including an e...

*Correspondence: [email protected] Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, China Abstract As a particular expression of stochastic delay differential equations, stochastic pantograph differential equations have been widely used in nonlinear dynamics, quantum mechanics, and electrodynamics. In this paper, we mainly study the stability of analytical solution...

This note extends and interprets a result of Saito and Mitsui [SIAM J. Numer. Anal., 33 (1996), pp. 2254–2267] for a method of Milstein. The result concerns mean-square stability on a stochastic differential equation test problem with multiplicative noise. The numerical method reduces to the Theta Method on deterministic problems. Saito and Mitsui showed that the deterministic A-stability prope...

The main aim of this paper is to investigate the exponential stability of the Euler method for a stochastic age-dependent population equations with Poisson random measures. It is proved that the Euler scheme is exponentially stable in mean square sense. An example is given for illustration. Keywords—Stochastic age-dependent population equations, Poisson random measures, Numerical solutions, Exp...

The main aim of this paper is to investigate the exponential stability of the Euler method for a stochastic age-dependent population equations with Poisson random measures. It is proved that the Euler scheme is exponentially stable in mean square sense. An example is given for illustration. Keywords—Stochastic age-dependent population equations, Poisson random measures, Numerical solutions, Exp...

This article considers the robust exponential stability of uncertain switched stochastic systems with time-delay. Both almost sure (sample) stability and stability in mean square are investigated. Based on Lyapunov functional methods and linear matrix inequality techniques, new criteria for exponential robust stability of switched stochastic delay systems with non-linear uncertainties are deriv...