Stabilization of Periodical Discrete Feedback Control for Markov Jumping Stochastic Systems

Motivated by the two strategies of intermittent control and discrete feedback control, this paper aims to introduce a periodically intermittent discrete feedback control in the drift part to stabilize an unstable Markov jumping stochastic differential system. It is illustrated that, by the approach of comparison principle, this can be achieved in the sense of almost sure exponential stability. Further, the stabilization theory is applied to Markov jumping stochastic recurrent neural networks.

Numerical method of highly nonlinear and nonautonomous neutral stochastic differential delay equations with Markovian switching

In this paper, we establish a partially truncated Euler–Maruyama scheme for highly nonlinear and nonautonomous neutral stochastic differential delay equations with Markovian switching. We investigate the strong convergence rate and almost sure exponential stability of the numerical solutions under the generalized Khasminskii-type condition.

Existence, Uniqueness, and Almost Sure Exponential Stability of Solutions to Nonlinear Stochastic System with Markovian Switching and Lévy Noises

This paper is concerned with existence, uniqueness, and almost sure exponential stability of solutions to nonlinear stochastic system with Markovian switching and Lévy noises. Firstly, the existence and uniqueness of solutions to the system is studied. Then, the almost sure exponential stability of the system is derived. Finally, an example is presented to illustrate the results.