Thesis

Analysis, approximation and control of hybrid stochastic systems

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Awarding institution
  • University of Strathclyde
Date of award
  • 2026
Thesis identifier
  • T18175
Person Identifier (Local)
  • 202274545
Qualification Level
Qualification Name
Department, School or Faculty
Abstract
  • Hybrid stochastic systems involving memory effects and Markovian switching have been widely used to model a variety of dynamical systems arising in science and engineering. This thesis addresses two fundamental problems in the study of hybrid stochastic systems: the numerical approximation of hybrid stochastic functional differential equations with infinite time delay and the stabilisation of hybrid stochastic differential equations by event-triggered control. For hybrid stochastic functional differential equations with infinite time delay, the convergence theory of the truncated Euler–Maruyama method is established under a local Lipschitz condition together with a Khasminskii-type condition. The analysis is further extended under a dissipative Khasminskii-type condition, leading to a strong convergence theory over the entire range q ∈ [1, p). Under suitable additional conditions, convergence rate estimates are also obtained. For hybrid stochastic differential equations, an event-triggered control framework based on trajectories of discrete-time observations is developed. Both state-feedback and output-feedback controllers are considered. By establishing a connection between the event-triggered controlled system and a corresponding uncertain stochastic system, sufficient conditions guaranteeing exponential mean-square stability are derived. Taken together, the work presented in this thesis broadens the existing theory for hybrid stochastic systems by extending the convergence theory for numerical methods under weaker assumptions and developing an event-triggered control framework based on discrete-time observations, thereby contributing to the analysis, numerical approximation and control of hybrid stochastic systems.
Advisor / supervisor
  • Mao, Xuerong
Resource Type
DOI

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