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Title: Stability Analysis and Controller Design of Linear Systems with Random Parametric Uncertainties
Keywords: Uncertain Systems, Stability, Distribution Control, Random Parametric Uncertainties, Generalized Polynomial Chaos Theory, Probabilistic Robust Control
Issue Date: 22-Mar-2013
Citation: LI XIAOYANG (2013-03-22). Stability Analysis and Controller Design of Linear Systems with Random Parametric Uncertainties. ScholarBank@NUS Repository.
Abstract: This thesis studies the stability analysis and distribution control of systems with random parametric uncertainties. Being set under the framework of the generalized polynomial chaos (gPC) theory, the novelty of this thesis is that it attempts to interpret the effects of the random uncertainties in terms of the mutual influence between the nominal dynamics of the original system and the variations caused by the uncertainties. Sufficient conditions for asymptotic stochastic stability are derived, and are analyzed with two special cases of uncertainties following uniform and Beta distributions. Inspired by applications requiring the control of the probabilistic distribution of the system output, the distribution control of system state is also studied. Control algorithms with integral action are proposed for two types of desired random variables. This thesis provides a new approach for studying systems with parametric uncertainties, and demonstrates the application of gPC theory to system and control theory.
Appears in Collections:Ph.D Theses (Open)

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