Analysis on exponential stability of hybrid pantograph stochastic differential equations with highly nonlinear coefficients

Surong You, Wei Mao, Xuerong Mao, Liangjian Hu

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

This paper discusses exponential stability of solutions for highly nonlinear hybrid pantograph stochastic differential equations (PSDEs). Two criteria are proposed to guarantee exponential stability of the solution. The first criterion is a Khasminskii-type condition involving general Lyapunov functions. The second is developed on coefficients of the equation in virtue of M-matrix techniques. Based on the second criterion, robust stability of a perturbed hybrid PSDE is also investigated. The theory shows how much an exponentially stable hybrid PSDE can tolerate to remain stable.
LanguageEnglish
Pages73–83
Number of pages11
JournalApplied Mathematics and Computation
Volume263
Early online date21 May 2015
DOIs
Publication statusPublished - 15 Jul 2015

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Pantograph
Pantographs
Exponential Stability
Asymptotic stability
Stochastic Equations
Differential equations
Differential equation
Coefficient
Stability of Solutions
M-matrix
Robust Stability
Lyapunov functions
Lyapunov Function

Keywords

  • Brownian motion
  • Markov chain
  • hybrid pantograph stochastic differential equations
  • exponential stability
  • robust stability

Cite this

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title = "Analysis on exponential stability of hybrid pantograph stochastic differential equations with highly nonlinear coefficients",
abstract = "This paper discusses exponential stability of solutions for highly nonlinear hybrid pantograph stochastic differential equations (PSDEs). Two criteria are proposed to guarantee exponential stability of the solution. The first criterion is a Khasminskii-type condition involving general Lyapunov functions. The second is developed on coefficients of the equation in virtue of M-matrix techniques. Based on the second criterion, robust stability of a perturbed hybrid PSDE is also investigated. The theory shows how much an exponentially stable hybrid PSDE can tolerate to remain stable.",
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Analysis on exponential stability of hybrid pantograph stochastic differential equations with highly nonlinear coefficients. / You, Surong; Mao, Wei ; Mao, Xuerong; Hu, Liangjian.

In: Applied Mathematics and Computation, Vol. 263, 15.07.2015, p. 73–83.

Research output: Contribution to journalArticle

TY - JOUR

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AU - You, Surong

AU - Mao, Wei

AU - Mao, Xuerong

AU - Hu, Liangjian

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N2 - This paper discusses exponential stability of solutions for highly nonlinear hybrid pantograph stochastic differential equations (PSDEs). Two criteria are proposed to guarantee exponential stability of the solution. The first criterion is a Khasminskii-type condition involving general Lyapunov functions. The second is developed on coefficients of the equation in virtue of M-matrix techniques. Based on the second criterion, robust stability of a perturbed hybrid PSDE is also investigated. The theory shows how much an exponentially stable hybrid PSDE can tolerate to remain stable.

AB - This paper discusses exponential stability of solutions for highly nonlinear hybrid pantograph stochastic differential equations (PSDEs). Two criteria are proposed to guarantee exponential stability of the solution. The first criterion is a Khasminskii-type condition involving general Lyapunov functions. The second is developed on coefficients of the equation in virtue of M-matrix techniques. Based on the second criterion, robust stability of a perturbed hybrid PSDE is also investigated. The theory shows how much an exponentially stable hybrid PSDE can tolerate to remain stable.

KW - Brownian motion

KW - Markov chain

KW - hybrid pantograph stochastic differential equations

KW - exponential stability

KW - robust stability

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