TITLE:
Stabilization of Functional System with Markovian Switching
AUTHORS:
Lizhu Feng, Qiong Cai
KEYWORDS:
Stochastic Functional System; Brownian Noise; Markovian Switching; Boundedness; Stabilization
JOURNAL NAME:
Applied Mathematics,
Vol.4 No.11A,
November
27,
2013
ABSTRACT: There are many papers
related to stability, some on suppression or on stabilization are one type of
them. Functional differential systems are common and important in practice.
They are special situations of neutral differential systems and generalization
of ordinary differential systems. We discussed conditions on suppression on
functional system with Markovian switching in our previous work: “Suppression
of Functional System with Markovian Switching”. Based on it, by slightly modifying
and adding some conditions, we get this paper. In this paper, we will study a
functional system whose coefficient satisfies the local Lipschitz condition
and the one-sided polynomial growth condition under Markovian switching. By
introducing two appropriate intensity Brownian noise, we find the potential
explosion system stabilized.