Numerical stability analysis of linear stochastic delay differential equations using Chebyshev spectral continuous time approximation

Shahab Torkamani, Ehsan Samiei, Oleg Bobrenkov, Eric Butcher

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

In this paper, a numerical approach is developed for the stability analysis of linear stochastic delay differential equations (SDDEs) in the parameter space based on the Chebyshev Spectral Continuous Time Approximation (CSCTA) technique. The CSCTA method is used to approximate an infinite-dimensional linear SDDE as a set of linear stochastic differential equations (SDEs). The mean and mean-square stability concepts are employed for the stochastic stability analysis of the resulting SDE. For this purpose, a set of linear deterministic differential equations for both the first and second moments are obtained using the Ito differential rule. Two examples are provided: a first order SDDE with multiplicative stochastic excitation and a second order SDDE with both additive and multiplicative stochastic excitation. In both examples the stability charts obtained from the proposed approach match those obtained using the stochastic semi-discretization method as described by Elbeyli et al. (Commun Nonlinear Sci Numer Simul 10(1):85–94, 2005). In the first example the stability results obtained from both numerical approaches are found to be less conservative than the Lyapunov-based stability region obtained by Samiei et al. (Int J Dyn Control 1(1):64–80, 2013).

Original languageEnglish (US)
Pages (from-to)210-220
Number of pages11
JournalInternational Journal of Dynamics and Control
Volume2
Issue number2
DOIs
StatePublished - Jun 1 2014

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Stochastic Delay Differential Equations
Convergence of numerical methods
Numerical Stability
Chebyshev
Continuous Time
Numerical Analysis
Stability Analysis
Differential equations
Approximation
Differential equation
Stochastic Equations
Multiplicative
Excitation
Mean-square Stability
Semidiscretization
Stochastic Stability
Stability Region
Stochastic Analysis
Discretization Method
Chart

Keywords

  • Brownian motion process
  • Chebyshev spectral continuous time approximation
  • Moment stability
  • Semidiscretization
  • Time-delay
  • White noise

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Control and Systems Engineering
  • Electrical and Electronic Engineering
  • Mechanical Engineering
  • Control and Optimization
  • Modeling and Simulation

Cite this

Numerical stability analysis of linear stochastic delay differential equations using Chebyshev spectral continuous time approximation. / Torkamani, Shahab; Samiei, Ehsan; Bobrenkov, Oleg; Butcher, Eric.

In: International Journal of Dynamics and Control, Vol. 2, No. 2, 01.06.2014, p. 210-220.

Research output: Contribution to journalArticle

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