Title :
Exponential stability of nonlinear neutral stochastic differential equations with Markovian switching
Author :
Liu, Hongliang ; Wang, Hui ; Duan, Guangren
Author_Institution :
Dept. of Math. & Appl. Math., Harbin Normal Univ., Harbin, China
Abstract :
Neutral stochastic differential equations (NSDEs) have recently been studied intensively. Given that many systems are often subject to component failures of repairs, changing subsystem interconnections and abrupt environmental disturbances etc., the structure and parameters of underlying NSDEs may change abruptly. One way to model such abrupt changes is to use the continuous-time Markov chains. As a result, the underlying NSDE become NSDE with Markovian switching which are hybrid systems. So few results are known about the NSDEs with Markovian switching and the aim of this paper is to close this gap. In this paper, a new condition for the exponential stability in the mean-square sense of such systems is given, which improved the existed condition, and its proof also implies the almost sure stability of such systems.
Keywords :
Markov processes; asymptotic stability; differential equations; nonlinear equations; time-varying systems; Markovian switching; continuous-time Markov chains; environmental disturbances; exponential stability; hybrid systems; nonlinear neutral stochastic differential equations; Markov processes; Power system stability; Stability criteria; Switches; Thermal stability; Brownian motion; Exponential stability; Generalized Ito´s formula; Hybrid system; Markov chain;
Conference_Titel :
Intelligent Control and Automation (WCICA), 2011 9th World Congress on
Conference_Location :
Taipei
Print_ISBN :
978-1-61284-698-9
DOI :
10.1109/WCICA.2011.5970629