The Improved LaSalle-Type Theorems for Stochastic Differential Delay Equations

DOI10.1080/07362994.2012.684320zbMath1248.60065OpenAlexW2027591821MaRDI QIDQ2905353

Xuerong Mao, Xiaoyue Li

Publication date: 27 August 2012

Published in: Stochastic Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/07362994.2012.684320

zbMATH Keywords

stochastic differential delay equationsalmost-sure stability

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stability theory of functional-differential equations (34K20) Stochastic stability in control theory (93E15) Stochastic functional-differential equations (34K50)

Related Items (13)

Asymptotic stability and boundedness of stochastic functional differential equations with Markovian switching ⋮ State feedback control for stochastic Markovian jump delay systems based on Lasalle-type theorem ⋮ Time-varying state-feedback stabilisation of stochastic feedforward nonlinear systems with unknown growth rate ⋮ Strong convergence and stability of backward Euler-Maruyama scheme for highly nonlinear hybrid stochastic differential delay equation ⋮ Event-triggered-based adaptive asymptotic tracking control for stochastic nonlinear time-delay systems with actuator and sensor faults ⋮ A new method for exponential stability of coupled reaction-diffusion systems with mixed delays: combining Razumikhin method with graph theory ⋮ Advances in the LaSalle-type theorems for stochastic functional differential equations with infinite delay ⋮ Decentralised adaptive output feedback stabilisation for stochastic time-delay systems via LaSalle-Yoshizawa-type theorem ⋮ The almost sure stability of coupled system of stochastic delay differential equations on networks ⋮ Convergence and asymptotic stability of an explicit numerical method for non-autonomous stochastic differential equations ⋮ The strong convergence and stability of explicit approximations for nonlinear stochastic delay differential equations ⋮ Adaptive state feedback control for time-delay stochastic nonlinear systems based on dynamic gain method ⋮ LaSalle-type theorems for stochastic functional differential equations with Markovian switching

Cites Work

• Generalised theory on asymptotic stability and boundedness of stochastic functional differential equations
• Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation
• Random differential inequalities
• Stochastic versions of the LaSalle theorem
• LaSalle-type theorems for stochastic differential delay equations
• Introduction to functional differential equations
• A note on the LaSalle-type theorems for stochastic differential delay equations
• The improved LaSalle-type theorems for stochastic functional differential equations
• Stability theory for ordinary differential equations
• Stochastic stability and control
• Stochastic Differential Equations with Markovian Switching
• Khasminskii-Type Theorems for Stochastic Differential Delay Equations
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