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Stabilization of highly nonlinear hybrid stochastic differential delay equations by periodically intermittent feedback controls based on discrete-time observations with asynchronous switching

Guangqiang Lan, Fansai Meng

Abstract

In this paper, we will investigate the moment exponential stabilization of highly nonlinear hybrid stochastic differential delay equations. A periodically intermittent controller based on discrete time state observations with asynchronous switching is designed. The upper bound of observation period as well as the lower bound of the control width are all obtained. Firstly, the finiteness and boundedness of the $p$-th moment of the solution are established under a generalized Khasminskii-type condition. Then reasonable conditions of control function, drift and diffusion coefficients are presented. Then exponential stability as well as the convergence rate of controlled system are proved. Finally, an example is presented to interpret the conclusion, which also indicates that the proportion of control interval has positive relation to the convergence rate.

Stabilization of highly nonlinear hybrid stochastic differential delay equations by periodically intermittent feedback controls based on discrete-time observations with asynchronous switching

Abstract

In this paper, we will investigate the moment exponential stabilization of highly nonlinear hybrid stochastic differential delay equations. A periodically intermittent controller based on discrete time state observations with asynchronous switching is designed. The upper bound of observation period as well as the lower bound of the control width are all obtained. Firstly, the finiteness and boundedness of the -th moment of the solution are established under a generalized Khasminskii-type condition. Then reasonable conditions of control function, drift and diffusion coefficients are presented. Then exponential stability as well as the convergence rate of controlled system are proved. Finally, an example is presented to interpret the conclusion, which also indicates that the proportion of control interval has positive relation to the convergence rate.
Paper Structure (5 sections, 4 theorems, 135 equations)

This paper contains 5 sections, 4 theorems, 135 equations.

Table of Contents

  1. Introduction
  2. Model description and Assumptions
  3. $q$-th moment finiteness and boundedness
  4. Main results
  5. An example

Key Result

Lemma 2.2

Let Assumption 1 holds. Then for any continuous function $\varphi:\left[ { - \tau ,T - h'} \right] \to {\mathbb{R}_+ }, T>h'>0,$ it follows that

Theorems & Definitions (4)

  • Lemma 2.2
  • Theorem 3.1
  • Lemma 3.2
  • Theorem 4.4