Moment exponential stability of random delay systems with two-time-scale Markovian switching
type: Item
instance of: scholarly article
title: Moment exponential stability of random delay systems with two-time-scale Markovian switching
zbMATH Open document ID: 1263.60062
author: Fuke Wu
author: G. Yin
author: Le Yi Wang
published in: Nonlinear Analysis. Real World Applications
publication date: 2012-12-28T00:00:00Z
review text: The authors consider the \(n\)-dimensional system with random delays \[ \dot{x}(t)= f(x(t), x(t- r(t))), \] where \(r(t)\geq 0\) is a continuous-time Markov chain in a finite state space \(\{r_1, r_2, \dotsc, r_m\}\). The system is a switching system along with the \(m\) fixed delay subsystems \[ \dot{y}(t) = f(y(t), y(t- r_i))\text{ for }i_1,2,\dotsc, m. \] The random switching is governed by the Markov chain \(r(t)\). They show that the fast changing part of the Markov switching, yields some average effect with respect to its stationary measure. Using the average system, a stability analysis is then carry out. The authors establish that the system has a weak limit in the sense of weak convergence of probability measures and also the Razumikhin-type theorem on the moment exponential stability.
reviewed by: Ruhollah Jahanipur
Mathematics Subject Classification ID: 60H25
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K50
Mathematics Subject Classification ID: 60J28
zbMATH DE Number: 6118794
zbMATH Keywords: random delay system
zbMATH Keywords: Razumikhin-type theorem
zbMATH Keywords: two-time-scale Markov chain
zbMATH Keywords: moment exponential stability
zbMATH Keywords: stationary distribution
MaRDI profile type: Publication
full work available at URL: j.nonrwa.2012.02.013
OpenAlex ID: W1977689264
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DOI: 10.1016/J.NONRWA.2012.02.013
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description: scientific article; zbMATH DE number 6118794