Stabilization in distribution of hybrid stochastic systems by intermittent feedback controls

In this paper, stabilization in distribution of hybrid stochastic differential equations (HSDEs) via periodically intermittent feedback controls is investigated. It is revealed that probability distributions of the solution will converge to a stationary distribution is revealed. Firstly, by using the theory of M-matrix and intermittent control strategy, we establish sufficient conditions for stabilization in distribution of HSDEs. Then, we prove the existence and uniqueness of invariant probability distribution, the lower bound of the intermittent parameter 8* is obtained. Three numerical examples are discussed to support our results of theoretical analysis. & COPY; 2023 Elsevier Ltd. All rights reserved.

Automated summary

This paper investigates the stabilization in distribution of hybrid stochastic differential equations (HSDEs) through periodically intermittent feedback controls. It is shown that the probability distributions of the solutions will converge to a stationary distribution. Firstly, sufficient conditions for stabilization in distribution of HSDEs are established using the theory of M-matrix and intermittent control strategy. Then, the existence and uniqueness of invariant probability distribution are proven, and the lower bound of the intermittent parameter 8* is obtained. Three numerical examples are discussed to support the theoretical analysis results.