Averaging and stability of quasilinear functional differential equations with Markov parameters

• Main Authors: Katafygiotis, Lambros S., Tsarkov, Yevgeny
• Format: Article in Journal/Newspaper
• Language: English
• Published: 1999
• Subjects: Averaging Procedures; Functional Differential Equations; Small Random Perturbations; Stochastic Stability; North Atlantic
• Online Access: http://repository.ust.hk/ir/Record/1783.1-25754; http://lbdiscover.ust.hk/uresolver?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rfr_id=info:sid/HKUST:SPI&rft.genre=article&rft.issn=1048-9533&rft.volume=12&rft.issue=1&rft.date=1999&rft.spage=1&rft.aulast=Katafygiotis&rft.aufirst=L.&rft.atitle=Averaging+and+stability+of+quasilinear+functional+differential+equations+with+Markov+parameters&rft.title=Journal+of+Applied+Mathematics+and+Stochastic+Analysis; http://www.scopus.com/record/display.url?eid=2-s2.0-53149144281&origin=inward

An asymptotic method for stability analysis of quasilinear functional differential equations, with small perturbations dependent on phase coordinates and an ergodic Markov process, is presented. The proposed method is based on an averaging procedure with respect to: 1) time along critical solutions of the linear equation; and 2) the invariant measure of the Markov process. For asymptotic analysis of the initial random equation with delay, it is proved that one can approximate its solutions (which are stochastic processes) by corresponding solutions of a specially constructed averaged, deterministic ordinary differential equation. Moreover, it is proved that exponential stability of the resulting deterministic equation is sufficient for exponential p-stability of the initial random system for all positive numbers p, and for sufficiently small perturbation terms. ©1999 by North Atlantic Science Publishing Company.