Abstract and Applied Analysis

Razumikhin-Type Theorems on Exponential Stability of SDDEs Containing Singularly Perturbed Random Processes

Junhao Hu, Xuerong Mao, and Chenggui Yuan

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Abstract

This paper concerns Razumikhin-type theorems on exponential stability of stochastic differential delay equations with Markovian switching, where the modulating Markov chain involves small parameters. The smaller the parameter is, the rapider switching the system will experience. In order to reduce the complexity, we will “replace” the original systems by limit systems with a simple structure. Under Razumikhin-type conditions, we establish theorems that if the limit systems are p th-moment exponentially stable; then, the original systems are p th-moment exponentially stable in an appropriate sense.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 854743, 12 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393449436

Digital Object Identifier
doi:10.1155/2013/854743

Mathematical Reviews number (MathSciNet)
MR3064338

Zentralblatt MATH identifier
1279.60069

Citation

Hu, Junhao; Mao, Xuerong; Yuan, Chenggui. Razumikhin-Type Theorems on Exponential Stability of SDDEs Containing Singularly Perturbed Random Processes. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 854743, 12 pages. doi:10.1155/2013/854743. https://projecteuclid.org/euclid.aaa/1393449436


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