Finite-time stability of stochastic nonlinear systems with Markovian switching

This paper presents a new Lyapunov theorem on almost surely finite-time stability for stochastic nonlinear systems with Markovian switching. Unlike the work in [3] that consider finite-time stability and stabilisation of conventional stochastic differential equation (SDE) systems, this paper aims to...

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Bibliographic Details
Main Authors: Juliang Yin, Xin Yu, Suiyang Khoo
Format: Conference Proceeding
Language:English
Subjects:
Differential equations
Finite-time stability
Lyapunov stability
Markov processes
Markovian switching
Mathematical model
Nonlinear systems
Stability analysis
Stochastic nonlinear systems
Switches
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Summary:This paper presents a new Lyapunov theorem on almost surely finite-time stability for stochastic nonlinear systems with Markovian switching. Unlike the work in [3] that consider finite-time stability and stabilisation of conventional stochastic differential equation (SDE) systems, this paper aims to propose a weaker finite-time stability theory for a more general class of SDE systems with Markovian switching. A lemma is presented to discuss conditions that ensure the existence of a unique strong solution for such SDE systems with Markovian switching. Extended Comparison Principle and Bihari's inequality are derived, which relaxes some previous conditions and play an important role in the proof of the new Lyapunov theorem. Weaker conditions are proposed to ensure finite-time stability in probability one with supportive examples. Two simulation examples are given to illustrate the theoretical analysis.
ISSN:2161-2927
DOI:10.23919/ChiCC.2017.8027634