Stabilization of highly nonlinear neutral stochastic systems with Markovian switching by periodically intermittent feedback control

Abstract

This article mainly studies the stabilization of highly nonlinear neutral stochastic systems with Markovian switching by using periodically intermittent feedback control, whose feedback control has a time delay. For a given unstable highly nonlinear neutral stochastic systems with Markovian switching, a periodically intermittent feedback control function is imposed. By using the Lyapunov function method, M-matrix and comparison principle, the pth moment exponential stability of highly nonlinear hybrid neutral stochastic systems is established. Finally, two numerical examples are provided to illustrate our theoretical analysis results.

Some Results of Stochastic Differential Equations

“…Global stabilization via output feedback of stochastic nonlinear time-delay systems with time-varying measurement error is established by [29]. Just recently, Zhao and Zhu [30,31] considered the stabilization of highly nonlinear neutral stochastic systems. The stabilization of the stochastic system is a hot issue.…”

Exponential stability of neutral hybrid nonlinear systems via aperiodically intermittent stochastic noise: Average skills

“…On the other hand, there is little existing work that discusses the joint effects of neutral term and Markov switching in aperodic intermittent control. Firstly, the system structure may not be invariant, and it is necessary to study Markov switching systems in order to model the abrupt changes of the system (see [3,5,9,14,16,20,21,26,28,29,31,33,35,41]). Secondly, a special class of stochastic differential equations called neutral stochastic differential equations has received much attention in the study of stochastic differential equations since the delay is included in their derivatives (see [2-4, 7, 9, 13, 29, 35]).…”

“…Secondly, a special class of stochastic differential equations called neutral stochastic differential equations has received much attention in the study of stochastic differential equations since the delay is included in their derivatives (see [2-4, 7, 9, 13, 29, 35]). Thus, the neutral hybrid stochastic systems play significant roles in the stochastic field (see [3,9,29,35,41]). For example, [41] investigated the stabilization of highly nonlinear neutral stochastic systems with Markov switching by using periodic intermittent feedback control.…”

“…Thus, the neutral hybrid stochastic systems play significant roles in the stochastic field (see [3,9,29,35,41]). For example, [41] investigated the stabilization of highly nonlinear neutral stochastic systems with Markov switching by using periodic intermittent feedback control. However, periodic intermittent control has some limitations, since aperiodic intermittent feedback control is recognized to be more effective in real control systems.…”